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1",[576,1055,1057,1078],{"className":1056,"ariaHidden":606},[605],[576,1058,1060,1064,1067,1071,1075],{"className":1059},[610],[576,1061],{"className":1062,"style":1063},[614],"height:0.6667em;vertical-align:-0.0833em;",[576,1065,597],{"className":1066},[619,620],[576,1068],{"className":1069,"style":1070},[886],"margin-right:0.2222em;",[576,1072,1048],{"className":1073},[1074],"mbin",[576,1076],{"className":1077,"style":1070},[886],[576,1079,1081,1084],{"className":1080},[610],[576,1082],{"className":1083,"style":649},[614],[576,1085,765],{"className":1086},[619]," Extremstellen.",[818,1089,1090,1091,1093,1094,1204,1205,1233,1234,1262,1263,1357,1358,1412],{},"Das ",[568,1092,553],{}," bestimmt allein der Summand ",[576,1095,1097,1123],{"className":1096},[579],[576,1098,1100],{"className":1099},[583],[585,1101,1102],{"xmlns":587},[589,1103,1104,1120],{},[592,1105,1106,1112],{},[671,1107,1108,1110],{},[595,1109,675],{},[595,1111,597],{},[1113,1114,1115,1118],"msup",{},[595,1116,1117],{},"x",[595,1119,597],{},[599,1121,1122],{"encoding":601},"a_n x^n",[576,1124,1126],{"className":1125,"ariaHidden":606},[605],[576,1127,1129,1133,1173],{"className":1128},[610],[576,1130],{"className":1131,"style":1132},[614],"height:0.8144em;vertical-align:-0.15em;",[576,1134,1136,1139],{"className":1135},[619],[576,1137,675],{"className":1138},[619,620],[576,1140,1142],{"className":1141},[700],[576,1143,1145,1165],{"className":1144},[704,705],[576,1146,1148,1162],{"className":1147},[709],[576,1149,1151],{"className":1150,"style":714},[713],[576,1152,1153,1156],{"style":717},[576,1154],{"className":1155,"style":722},[721],[576,1157,1159],{"className":1158},[726,727,728,729],[576,1160,597],{"className":1161},[619,620,729],[576,1163,737],{"className":1164},[736],[576,1166,1168],{"className":1167},[709],[576,1169,1171],{"className":1170,"style":744},[713],[576,1172],{},[576,1174,1176,1179],{"className":1175},[619],[576,1177,1117],{"className":1178},[619,620],[576,1180,1182],{"className":1181},[700],[576,1183,1185],{"className":1184},[704],[576,1186,1188],{"className":1187},[709],[576,1189,1192],{"className":1190,"style":1191},[713],"height:0.6644em;",[576,1193,1195,1198],{"style":1194},"top:-3.063em;margin-right:0.05em;",[576,1196],{"className":1197,"style":722},[721],[576,1199,1201],{"className":1200},[726,727,728,729],[576,1202,597],{"className":1203},[619,620,729],". Bei geradem ",[576,1206,1208,1221],{"className":1207},[579],[576,1209,1211],{"className":1210},[583],[585,1212,1213],{"xmlns":587},[589,1214,1215,1219],{},[592,1216,1217],{},[595,1218,597],{},[599,1220,597],{"encoding":601},[576,1222,1224],{"className":1223,"ariaHidden":606},[605],[576,1225,1227,1230],{"className":1226},[610],[576,1228],{"className":1229,"style":615},[614],[576,1231,597],{"className":1232},[619,620]," zeigen beide Enden des Graphen in dieselbe Richtung, bei ungeradem ",[576,1235,1237,1250],{"className":1236},[579],[576,1238,1240],{"className":1239},[583],[585,1241,1242],{"xmlns":587},[589,1243,1244,1248],{},[592,1245,1246],{},[595,1247,597],{},[599,1249,597],{"encoding":601},[576,1251,1253],{"className":1252,"ariaHidden":606},[605],[576,1254,1256,1259],{"className":1255},[610],[576,1257],{"className":1258,"style":615},[614],[576,1260,597],{"className":1261},[619,620]," in entgegengesetzte. Ist ",[576,1264,1266,1289],{"className":1265},[579],[576,1267,1269],{"className":1268},[583],[585,1270,1271],{"xmlns":587},[589,1272,1273,1286],{},[592,1274,1275,1281,1284],{},[671,1276,1277,1279],{},[595,1278,675],{},[595,1280,597],{},[837,1282,1283],{},">",[635,1285,637],{},[599,1287,1288],{"encoding":601},"a_n > 0",[576,1290,1292,1348],{"className":1291,"ariaHidden":606},[605],[576,1293,1295,1299,1339,1342,1345],{"className":1294},[610],[576,1296],{"className":1297,"style":1298},[614],"height:0.6891em;vertical-align:-0.15em;",[576,1300,1302,1305],{"className":1301},[619],[576,1303,675],{"className":1304},[619,620],[576,1306,1308],{"className":1307},[700],[576,1309,1311,1331],{"className":1310},[704,705],[576,1312,1314,1328],{"className":1313},[709],[576,1315,1317],{"className":1316,"style":714},[713],[576,1318,1319,1322],{"style":717},[576,1320],{"className":1321,"style":722},[721],[576,1323,1325],{"className":1324},[726,727,728,729],[576,1326,597],{"className":1327},[619,620,729],[576,1329,737],{"className":1330},[736],[576,1332,1334],{"className":1333},[709],[576,1335,1337],{"className":1336,"style":744},[713],[576,1338],{},[576,1340],{"className":1341,"style":887},[886],[576,1343,1283],{"className":1344},[891],[576,1346],{"className":1347,"style":887},[886],[576,1349,1351,1354],{"className":1350},[610],[576,1352],{"className":1353,"style":649},[614],[576,1355,637],{"className":1356},[619],", geht der Graph für ",[576,1359,1361,1382],{"className":1360},[579],[576,1362,1364],{"className":1363},[583],[585,1365,1366],{"xmlns":587},[589,1367,1368,1379],{},[592,1369,1370,1372,1375],{},[595,1371,1117],{},[837,1373,1374],{},"→",[595,1376,1378],{"mathvariant":1377},"normal","∞",[599,1380,1381],{"encoding":601},"x \\to \\infty",[576,1383,1385,1403],{"className":1384,"ariaHidden":606},[605],[576,1386,1388,1391,1394,1397,1400],{"className":1387},[610],[576,1389],{"className":1390,"style":615},[614],[576,1392,1117],{"className":1393},[619,620],[576,1395],{"className":1396,"style":887},[886],[576,1398,1374],{"className":1399},[891],[576,1401],{"className":1402,"style":887},[886],[576,1404,1406,1409],{"className":1405},[610],[576,1407],{"className":1408,"style":615},[614],[576,1410,1378],{"className":1411},[619]," nach oben.",[818,1414,1415],{},"Kommen nur gerade Exponenten vor, ist der Graph achsensymmetrisch zur y-Achse; kommen nur ungerade vor, ist er punktsymmetrisch zum Ursprung.",[559,1417,1419],{"id":1418},"beispiele","Beispiele",[564,1421,1422,1612,1613,1641,1642,1670,1671,1763,1764,1798],{},[576,1423,1425,1474],{"className":1424},[579],[576,1426,1428],{"className":1427},[583],[585,1429,1430],{"xmlns":587},[589,1431,1432,1471],{},[592,1433,1434,1436,1438,1440,1442,1444,1446,1453,1455,1458,1464,1466,1469],{},[595,1435,835],{},[837,1437,840],{"stretchy":839},[595,1439,1117],{},[837,1441,845],{"stretchy":839},[837,1443,848],{},[635,1445,795],{},[1113,1447,1448,1450],{},[595,1449,1117],{},[635,1451,1452],{},"3",[837,1454,1048],{},[635,1456,1457],{},"4",[1113,1459,1460,1462],{},[595,1461,1117],{},[635,1463,795],{},[837,1465,1048],{},[635,1467,1468],{},"6",[595,1470,1117],{},[599,1472,1473],{"encoding":601},"f(x) = 2x^3 - 4x^2 - 6x",[576,1475,1477,1504,1553,1600],{"className":1476,"ariaHidden":606},[605],[576,1478,1480,1483,1486,1489,1492,1495,1498,1501],{"className":1479},[610],[576,1481],{"className":1482,"style":867},[614],[576,1484,835],{"className":1485,"style":871},[619,620],[576,1487,840],{"className":1488},[875],[576,1490,1117],{"className":1491},[619,620],[576,1493,845],{"className":1494},[882],[576,1496],{"className":1497,"style":887},[886],[576,1499,848],{"className":1500},[891],[576,1502],{"className":1503,"style":887},[886],[576,1505,1507,1511,1514,1544,1547,1550],{"className":1506},[610],[576,1508],{"className":1509,"style":1510},[614],"height:0.8974em;vertical-align:-0.0833em;",[576,1512,795],{"className":1513},[619],[576,1515,1517,1520],{"className":1516},[619],[576,1518,1117],{"className":1519},[619,620],[576,1521,1523],{"className":1522},[700],[576,1524,1526],{"className":1525},[704],[576,1527,1529],{"className":1528},[709],[576,1530,1533],{"className":1531,"style":1532},[713],"height:0.8141em;",[576,1534,1535,1538],{"style":1194},[576,1536],{"className":1537,"style":722},[721],[576,1539,1541],{"className":1540},[726,727,728,729],[576,1542,1452],{"className":1543},[619,729],[576,1545],{"className":1546,"style":1070},[886],[576,1548,1048],{"className":1549},[1074],[576,1551],{"className":1552,"style":1070},[886],[576,1554,1556,1559,1562,1591,1594,1597],{"className":1555},[610],[576,1557],{"className":1558,"style":1510},[614],[576,1560,1457],{"className":1561},[619],[576,1563,1565,1568],{"className":1564},[619],[576,1566,1117],{"className":1567},[619,620],[576,1569,1571],{"className":1570},[700],[576,1572,1574],{"className":1573},[704],[576,1575,1577],{"className":1576},[709],[576,1578,1580],{"className":1579,"style":1532},[713],[576,1581,1582,1585],{"style":1194},[576,1583],{"className":1584,"style":722},[721],[576,1586,1588],{"className":1587},[726,727,728,729],[576,1589,795],{"className":1590},[619,729],[576,1592],{"className":1593,"style":1070},[886],[576,1595,1048],{"className":1596},[1074],[576,1598],{"className":1599,"style":1070},[886],[576,1601,1603,1606,1609],{"className":1602},[610],[576,1604],{"className":1605,"style":649},[614],[576,1607,1468],{"className":1608},[619],[576,1610,1117],{"className":1611},[619,620]," hat den Grad ",[576,1614,1616,1629],{"className":1615},[579],[576,1617,1619],{"className":1618},[583],[585,1620,1621],{"xmlns":587},[589,1622,1623,1627],{},[592,1624,1625],{},[635,1626,1452],{},[599,1628,1452],{"encoding":601},[576,1630,1632],{"className":1631,"ariaHidden":606},[605],[576,1633,1635,1638],{"className":1634},[610],[576,1636],{"className":1637,"style":649},[614],[576,1639,1452],{"className":1640},[619]," und den Leitkoeffizienten ",[576,1643,1645,1658],{"className":1644},[579],[576,1646,1648],{"className":1647},[583],[585,1649,1650],{"xmlns":587},[589,1651,1652,1656],{},[592,1653,1654],{},[635,1655,795],{},[599,1657,795],{"encoding":601},[576,1659,1661],{"className":1660,"ariaHidden":606},[605],[576,1662,1664,1667],{"className":1663},[610],[576,1665],{"className":1666,"style":649},[614],[576,1668,795],{"className":1669},[619],". Weil ",[576,1672,1674,1696],{"className":1673},[579],[576,1675,1677],{"className":1676},[583],[585,1678,1679],{"xmlns":587},[589,1680,1681,1693],{},[592,1682,1683,1689,1691],{},[671,1684,1685,1687],{},[595,1686,675],{},[635,1688,637],{},[837,1690,848],{},[635,1692,637],{},[599,1694,1695],{"encoding":601},"a_0 = 0",[576,1697,1699,1754],{"className":1698,"ariaHidden":606},[605],[576,1700,1702,1705,1745,1748,1751],{"className":1701},[610],[576,1703],{"className":1704,"style":690},[614],[576,1706,1708,1711],{"className":1707},[619],[576,1709,675],{"className":1710},[619,620],[576,1712,1714],{"className":1713},[700],[576,1715,1717,1737],{"className":1716},[704,705],[576,1718,1720,1734],{"className":1719},[709],[576,1721,1723],{"className":1722,"style":919},[713],[576,1724,1725,1728],{"style":717},[576,1726],{"className":1727,"style":722},[721],[576,1729,1731],{"className":1730},[726,727,728,729],[576,1732,637],{"className":1733},[619,729],[576,1735,737],{"className":1736},[736],[576,1738,1740],{"className":1739},[709],[576,1741,1743],{"className":1742,"style":744},[713],[576,1744],{},[576,1746],{"className":1747,"style":887},[886],[576,1749,848],{"className":1750},[891],[576,1752],{"className":1753,"style":887},[886],[576,1755,1757,1760],{"className":1756},[610],[576,1758],{"className":1759,"style":649},[614],[576,1761,637],{"className":1762},[619]," ist, geht der Graph durch den Ursprung. Für die Nullstellen klammert man ",[576,1765,1767,1783],{"className":1766},[579],[576,1768,1770],{"className":1769},[583],[585,1771,1772],{"xmlns":587},[589,1773,1774,1780],{},[592,1775,1776,1778],{},[635,1777,795],{},[595,1779,1117],{},[599,1781,1782],{"encoding":601},"2x",[576,1784,1786],{"className":1785,"ariaHidden":606},[605],[576,1787,1789,1792,1795],{"className":1788},[610],[576,1790],{"className":1791,"style":649},[614],[576,1793,795],{"className":1794},[619],[576,1796,1117],{"className":1797},[619,620]," aus und zerlegt den Rest in Linearfaktoren:",[576,1800,1803],{"className":1801},[1802],"katex-display",[576,1804,1806,1882],{"className":1805},[579],[576,1807,1809],{"className":1808},[583],[585,1810,1812],{"xmlns":587,"display":1811},"block",[589,1813,1814,1879],{},[592,1815,1816,1818,1820,1822,1824,1826,1828,1830,1852,1854,1856,1858,1860,1862,1864,1866,1868,1870,1872,1875,1877],{},[595,1817,835],{},[837,1819,840],{"stretchy":839},[595,1821,1117],{},[837,1823,845],{"stretchy":839},[837,1825,848],{},[635,1827,795],{},[595,1829,1117],{},[592,1831,1832,1834,1840,1842,1844,1846,1848,1850],{},[837,1833,840],{"fence":606},[1113,1835,1836,1838],{},[595,1837,1117],{},[635,1839,795],{},[837,1841,1048],{},[635,1843,795],{},[595,1845,1117],{},[837,1847,1048],{},[635,1849,1452],{},[837,1851,845],{"fence":606},[837,1853,848],{},[635,1855,795],{},[595,1857,1117],{},[837,1859,840],{"stretchy":839},[595,1861,1117],{},[837,1863,1048],{},[635,1865,1452],{},[837,1867,845],{"stretchy":839},[837,1869,840],{"stretchy":839},[595,1871,1117],{},[837,1873,1874],{},"+",[635,1876,765],{},[837,1878,845],{"stretchy":839},[599,1880,1881],{"encoding":601},"f(x) = 2x \\left(x^2 - 2x - 3\\right) = 2x(x - 3)(x + 1)",[576,1883,1885,1912,2016,2043,2070],{"className":1884,"ariaHidden":606},[605],[576,1886,1888,1891,1894,1897,1900,1903,1906,1909],{"className":1887},[610],[576,1889],{"className":1890,"style":867},[614],[576,1892,835],{"className":1893,"style":871},[619,620],[576,1895,840],{"className":1896},[875],[576,1898,1117],{"className":1899},[619,620],[576,1901,845],{"className":1902},[882],[576,1904],{"className":1905,"style":887},[886],[576,1907,848],{"className":1908},[891],[576,1910],{"className":1911,"style":887},[886],[576,1913,1915,1919,1922,1925,1929,2007,2010,2013],{"className":1914},[610],[576,1916],{"className":1917,"style":1918},[614],"height:1.2141em;vertical-align:-0.35em;",[576,1920,795],{"className":1921},[619],[576,1923,1117],{"className":1924},[619,620],[576,1926],{"className":1927,"style":1928},[886],"margin-right:0.1667em;",[576,1930,1933,1943,1974,1977,1980,1983,1986,1989,1992,1995,1998,2001],{"className":1931},[1932],"minner",[576,1934,1938],{"className":1935,"style":1937},[875,1936],"delimcenter","top:0em;",[576,1939,840],{"className":1940},[1941,1942],"delimsizing","size1",[576,1944,1946,1949],{"className":1945},[619],[576,1947,1117],{"className":1948},[619,620],[576,1950,1952],{"className":1951},[700],[576,1953,1955],{"className":1954},[704],[576,1956,1958],{"className":1957},[709],[576,1959,1962],{"className":1960,"style":1961},[713],"height:0.8641em;",[576,1963,1965,1968],{"style":1964},"top:-3.113em;margin-right:0.05em;",[576,1966],{"className":1967,"style":722},[721],[576,1969,1971],{"className":1970},[726,727,728,729],[576,1972,795],{"className":1973},[619,729],[576,1975],{"className":1976,"style":1070},[886],[576,1978,1048],{"className":1979},[1074],[576,1981],{"className":1982,"style":1070},[886],[576,1984,795],{"className":1985},[619],[576,1987,1117],{"className":1988},[619,620],[576,1990],{"className":1991,"style":1070},[886],[576,1993,1048],{"className":1994},[1074],[576,1996],{"className":1997,"style":1070},[886],[576,1999,1452],{"className":2000},[619],[576,2002,2004],{"className":2003,"style":1937},[882,1936],[576,2005,845],{"className":2006},[1941,1942],[576,2008],{"className":2009,"style":887},[886],[576,2011,848],{"className":2012},[891],[576,2014],{"className":2015,"style":887},[886],[576,2017,2019,2022,2025,2028,2031,2034,2037,2040],{"className":2018},[610],[576,2020],{"className":2021,"style":867},[614],[576,2023,795],{"className":2024},[619],[576,2026,1117],{"className":2027},[619,620],[576,2029,840],{"className":2030},[875],[576,2032,1117],{"className":2033},[619,620],[576,2035],{"className":2036,"style":1070},[886],[576,2038,1048],{"className":2039},[1074],[576,2041],{"className":2042,"style":1070},[886],[576,2044,2046,2049,2052,2055,2058,2061,2064,2067],{"className":2045},[610],[576,2047],{"className":2048,"style":867},[614],[576,2050,1452],{"className":2051},[619],[576,2053,845],{"className":2054},[882],[576,2056,840],{"className":2057},[875],[576,2059,1117],{"className":2060},[619,620],[576,2062],{"className":2063,"style":1070},[886],[576,2065,1874],{"className":2066},[1074],[576,2068],{"className":2069,"style":1070},[886],[576,2071,2073,2076,2079],{"className":2072},[610],[576,2074],{"className":2075,"style":867},[614],[576,2077,765],{"className":2078},[619],[576,2080,845],{"className":2081},[882],[564,2083,2084,2085,2183,2184,2276,2277,2369,2370,2398,2399,810],{},"Die Nullstellen sind ",[576,2086,2088,2112],{"className":2087},[579],[576,2089,2091],{"className":2090},[583],[585,2092,2093],{"xmlns":587},[589,2094,2095,2109],{},[592,2096,2097,2103,2105,2107],{},[671,2098,2099,2101],{},[595,2100,1117],{},[635,2102,765],{},[837,2104,848],{},[837,2106,1048],{},[635,2108,765],{},[599,2110,2111],{"encoding":601},"x_1 = -1",[576,2113,2115,2170],{"className":2114,"ariaHidden":606},[605],[576,2116,2118,2121,2161,2164,2167],{"className":2117},[610],[576,2119],{"className":2120,"style":690},[614],[576,2122,2124,2127],{"className":2123},[619],[576,2125,1117],{"className":2126},[619,620],[576,2128,2130],{"className":2129},[700],[576,2131,2133,2153],{"className":2132},[704,705],[576,2134,2136,2150],{"className":2135},[709],[576,2137,2139],{"className":2138,"style":919},[713],[576,2140,2141,2144],{"style":717},[576,2142],{"className":2143,"style":722},[721],[576,2145,2147],{"className":2146},[726,727,728,729],[576,2148,765],{"className":2149},[619,729],[576,2151,737],{"className":2152},[736],[576,2154,2156],{"className":2155},[709],[576,2157,2159],{"className":2158,"style":744},[713],[576,2160],{},[576,2162],{"className":2163,"style":887},[886],[576,2165,848],{"className":2166},[891],[576,2168],{"className":2169,"style":887},[886],[576,2171,2173,2177,2180],{"className":2172},[610],[576,2174],{"className":2175,"style":2176},[614],"height:0.7278em;vertical-align:-0.0833em;",[576,2178,1048],{"className":2179},[619],[576,2181,765],{"className":2182},[619],", ",[576,2185,2187,2209],{"className":2186},[579],[576,2188,2190],{"className":2189},[583],[585,2191,2192],{"xmlns":587},[589,2193,2194,2206],{},[592,2195,2196,2202,2204],{},[671,2197,2198,2200],{},[595,2199,1117],{},[635,2201,795],{},[837,2203,848],{},[635,2205,637],{},[599,2207,2208],{"encoding":601},"x_2 = 0",[576,2210,2212,2267],{"className":2211,"ariaHidden":606},[605],[576,2213,2215,2218,2258,2261,2264],{"className":2214},[610],[576,2216],{"className":2217,"style":690},[614],[576,2219,2221,2224],{"className":2220},[619],[576,2222,1117],{"className":2223},[619,620],[576,2225,2227],{"className":2226},[700],[576,2228,2230,2250],{"className":2229},[704,705],[576,2231,2233,2247],{"className":2232},[709],[576,2234,2236],{"className":2235,"style":919},[713],[576,2237,2238,2241],{"style":717},[576,2239],{"className":2240,"style":722},[721],[576,2242,2244],{"className":2243},[726,727,728,729],[576,2245,795],{"className":2246},[619,729],[576,2248,737],{"className":2249},[736],[576,2251,2253],{"className":2252},[709],[576,2254,2256],{"className":2255,"style":744},[713],[576,2257],{},[576,2259],{"className":2260,"style":887},[886],[576,2262,848],{"className":2263},[891],[576,2265],{"className":2266,"style":887},[886],[576,2268,2270,2273],{"className":2269},[610],[576,2271],{"className":2272,"style":649},[614],[576,2274,637],{"className":2275},[619]," und ",[576,2278,2280,2302],{"className":2279},[579],[576,2281,2283],{"className":2282},[583],[585,2284,2285],{"xmlns":587},[589,2286,2287,2299],{},[592,2288,2289,2295,2297],{},[671,2290,2291,2293],{},[595,2292,1117],{},[635,2294,1452],{},[837,2296,848],{},[635,2298,1452],{},[599,2300,2301],{"encoding":601},"x_3 = 3",[576,2303,2305,2360],{"className":2304,"ariaHidden":606},[605],[576,2306,2308,2311,2351,2354,2357],{"className":2307},[610],[576,2309],{"className":2310,"style":690},[614],[576,2312,2314,2317],{"className":2313},[619],[576,2315,1117],{"className":2316},[619,620],[576,2318,2320],{"className":2319},[700],[576,2321,2323,2343],{"className":2322},[704,705],[576,2324,2326,2340],{"className":2325},[709],[576,2327,2329],{"className":2328,"style":919},[713],[576,2330,2331,2334],{"style":717},[576,2332],{"className":2333,"style":722},[721],[576,2335,2337],{"className":2336},[726,727,728,729],[576,2338,1452],{"className":2339},[619,729],[576,2341,737],{"className":2342},[736],[576,2344,2346],{"className":2345},[709],[576,2347,2349],{"className":2348,"style":744},[713],[576,2350],{},[576,2352],{"className":2353,"style":887},[886],[576,2355,848],{"className":2356},[891],[576,2358],{"className":2359,"style":887},[886],[576,2361,2363,2366],{"className":2362},[610],[576,2364],{"className":2365,"style":649},[614],[576,2367,1452],{"className":2368},[619],", also die Höchstzahl ",[576,2371,2373,2386],{"className":2372},[579],[576,2374,2376],{"className":2375},[583],[585,2377,2378],{"xmlns":587},[589,2379,2380,2384],{},[592,2381,2382],{},[635,2383,1452],{},[599,2385,1452],{"encoding":601},[576,2387,2389],{"className":2388,"ariaHidden":606},[605],[576,2390,2392,2395],{"className":2391},[610],[576,2393],{"className":2394,"style":649},[614],[576,2396,1452],{"className":2397},[619],". Außerdem ist ",[576,2400,2402,2442],{"className":2401},[579],[576,2403,2405],{"className":2404},[583],[585,2406,2407],{"xmlns":587},[589,2408,2409,2439],{},[592,2410,2411,2413,2415,2417,2419,2421,2424,2426,2428,2430,2433,2435,2437],{},[595,2412,835],{},[837,2414,840],{"stretchy":839},[635,2416,795],{},[837,2418,845],{"stretchy":839},[837,2420,848],{},[635,2422,2423],{},"16",[837,2425,1048],{},[635,2427,2423],{},[837,2429,1048],{},[635,2431,2432],{},"12",[837,2434,848],{},[837,2436,1048],{},[635,2438,2432],{},[599,2440,2441],{"encoding":601},"f(2) = 16 - 16 - 12 = -12",[576,2443,2445,2472,2490,2508,2526],{"className":2444,"ariaHidden":606},[605],[576,2446,2448,2451,2454,2457,2460,2463,2466,2469],{"className":2447},[610],[576,2449],{"className":2450,"style":867},[614],[576,2452,835],{"className":2453,"style":871},[619,620],[576,2455,840],{"className":2456},[875],[576,2458,795],{"className":2459},[619],[576,2461,845],{"className":2462},[882],[576,2464],{"className":2465,"style":887},[886],[576,2467,848],{"className":2468},[891],[576,2470],{"className":2471,"style":887},[886],[576,2473,2475,2478,2481,2484,2487],{"className":2474},[610],[576,2476],{"className":2477,"style":2176},[614],[576,2479,2423],{"className":2480},[619],[576,2482],{"className":2483,"style":1070},[886],[576,2485,1048],{"className":2486},[1074],[576,2488],{"className":2489,"style":1070},[886],[576,2491,2493,2496,2499,2502,2505],{"className":2492},[610],[576,2494],{"className":2495,"style":2176},[614],[576,2497,2423],{"className":2498},[619],[576,2500],{"className":2501,"style":1070},[886],[576,2503,1048],{"className":2504},[1074],[576,2506],{"className":2507,"style":1070},[886],[576,2509,2511,2514,2517,2520,2523],{"className":2510},[610],[576,2512],{"className":2513,"style":649},[614],[576,2515,2432],{"className":2516},[619],[576,2518],{"className":2519,"style":887},[886],[576,2521,848],{"className":2522},[891],[576,2524],{"className":2525,"style":887},[886],[576,2527,2529,2532,2535],{"className":2528},[610],[576,2530],{"className":2531,"style":2176},[614],[576,2533,1048],{"className":2534},[619],[576,2536,2432],{"className":2537},[619],[564,2539,2540,2541,2592,2593,2708,2709,2765,2766,2837,2838,2765,2888,2954,2955,2276,3056,810],{},"Verhalten im Unendlichen: ",[576,2542,2544,2562],{"className":2543},[579],[576,2545,2547],{"className":2546},[583],[585,2548,2549],{"xmlns":587},[589,2550,2551,2559],{},[592,2552,2553,2555,2557],{},[595,2554,597],{},[837,2556,848],{},[635,2558,1452],{},[599,2560,2561],{"encoding":601},"n = 3",[576,2563,2565,2583],{"className":2564,"ariaHidden":606},[605],[576,2566,2568,2571,2574,2577,2580],{"className":2567},[610],[576,2569],{"className":2570,"style":615},[614],[576,2572,597],{"className":2573},[619,620],[576,2575],{"className":2576,"style":887},[886],[576,2578,848],{"className":2579},[891],[576,2581],{"className":2582,"style":887},[886],[576,2584,2586,2589],{"className":2585},[610],[576,2587],{"className":2588,"style":649},[614],[576,2590,1452],{"className":2591},[619]," ist ungerade und ",[576,2594,2596,2622],{"className":2595},[579],[576,2597,2599],{"className":2598},[583],[585,2600,2601],{"xmlns":587},[589,2602,2603,2619],{},[592,2604,2605,2611,2613,2615,2617],{},[671,2606,2607,2609],{},[595,2608,675],{},[635,2610,1452],{},[837,2612,848],{},[635,2614,795],{},[837,2616,1283],{},[635,2618,637],{},[599,2620,2621],{"encoding":601},"a_3 = 2 > 0",[576,2623,2625,2680,2699],{"className":2624,"ariaHidden":606},[605],[576,2626,2628,2631,2671,2674,2677],{"className":2627},[610],[576,2629],{"className":2630,"style":690},[614],[576,2632,2634,2637],{"className":2633},[619],[576,2635,675],{"className":2636},[619,620],[576,2638,2640],{"className":2639},[700],[576,2641,2643,2663],{"className":2642},[704,705],[576,2644,2646,2660],{"className":2645},[709],[576,2647,2649],{"className":2648,"style":919},[713],[576,2650,2651,2654],{"style":717},[576,2652],{"className":2653,"style":722},[721],[576,2655,2657],{"className":2656},[726,727,728,729],[576,2658,1452],{"className":2659},[619,729],[576,2661,737],{"className":2662},[736],[576,2664,2666],{"className":2665},[709],[576,2667,2669],{"className":2668,"style":744},[713],[576,2670],{},[576,2672],{"className":2673,"style":887},[886],[576,2675,848],{"className":2676},[891],[576,2678],{"className":2679,"style":887},[886],[576,2681,2683,2687,2690,2693,2696],{"className":2682},[610],[576,2684],{"className":2685,"style":2686},[614],"height:0.6835em;vertical-align:-0.0391em;",[576,2688,795],{"className":2689},[619],[576,2691],{"className":2692,"style":887},[886],[576,2694,1283],{"className":2695},[891],[576,2697],{"className":2698,"style":887},[886],[576,2700,2702,2705],{"className":2701},[610],[576,2703],{"className":2704,"style":649},[614],[576,2706,637],{"className":2707},[619],". Für ",[576,2710,2712,2732],{"className":2711},[579],[576,2713,2715],{"className":2714},[583],[585,2716,2717],{"xmlns":587},[589,2718,2719,2729],{},[592,2720,2721,2723,2725,2727],{},[595,2722,1117],{},[837,2724,1374],{},[837,2726,1048],{},[595,2728,1378],{"mathvariant":1377},[599,2730,2731],{"encoding":601},"x \\to -\\infty",[576,2733,2735,2753],{"className":2734,"ariaHidden":606},[605],[576,2736,2738,2741,2744,2747,2750],{"className":2737},[610],[576,2739],{"className":2740,"style":615},[614],[576,2742,1117],{"className":2743},[619,620],[576,2745],{"className":2746,"style":887},[886],[576,2748,1374],{"className":2749},[891],[576,2751],{"className":2752,"style":887},[886],[576,2754,2756,2759,2762],{"className":2755},[610],[576,2757],{"className":2758,"style":1063},[614],[576,2760,1048],{"className":2761},[619],[576,2763,1378],{"className":2764},[619]," geht ",[576,2767,2769,2795],{"className":2768},[579],[576,2770,2772],{"className":2771},[583],[585,2773,2774],{"xmlns":587},[589,2775,2776,2792],{},[592,2777,2778,2780,2782,2784,2786,2788,2790],{},[595,2779,835],{},[837,2781,840],{"stretchy":839},[595,2783,1117],{},[837,2785,845],{"stretchy":839},[837,2787,1374],{},[837,2789,1048],{},[595,2791,1378],{"mathvariant":1377},[599,2793,2794],{"encoding":601},"f(x) \\to -\\infty",[576,2796,2798,2825],{"className":2797,"ariaHidden":606},[605],[576,2799,2801,2804,2807,2810,2813,2816,2819,2822],{"className":2800},[610],[576,2802],{"className":2803,"style":867},[614],[576,2805,835],{"className":2806,"style":871},[619,620],[576,2808,840],{"className":2809},[875],[576,2811,1117],{"className":2812},[619,620],[576,2814,845],{"className":2815},[882],[576,2817],{"className":2818,"style":887},[886],[576,2820,1374],{"className":2821},[891],[576,2823],{"className":2824,"style":887},[886],[576,2826,2828,2831,2834],{"className":2827},[610],[576,2829],{"className":2830,"style":1063},[614],[576,2832,1048],{"className":2833},[619],[576,2835,1378],{"className":2836},[619],", für ",[576,2839,2841,2858],{"className":2840},[579],[576,2842,2844],{"className":2843},[583],[585,2845,2846],{"xmlns":587},[589,2847,2848,2856],{},[592,2849,2850,2852,2854],{},[595,2851,1117],{},[837,2853,1374],{},[595,2855,1378],{"mathvariant":1377},[599,2857,1381],{"encoding":601},[576,2859,2861,2879],{"className":2860,"ariaHidden":606},[605],[576,2862,2864,2867,2870,2873,2876],{"className":2863},[610],[576,2865],{"className":2866,"style":615},[614],[576,2868,1117],{"className":2869},[619,620],[576,2871],{"className":2872,"style":887},[886],[576,2874,1374],{"className":2875},[891],[576,2877],{"className":2878,"style":887},[886],[576,2880,2882,2885],{"className":2881},[610],[576,2883],{"className":2884,"style":615},[614],[576,2886,1378],{"className":2887},[619],[576,2889,2891,2915],{"className":2890},[579],[576,2892,2894],{"className":2893},[583],[585,2895,2896],{"xmlns":587},[589,2897,2898,2912],{},[592,2899,2900,2902,2904,2906,2908,2910],{},[595,2901,835],{},[837,2903,840],{"stretchy":839},[595,2905,1117],{},[837,2907,845],{"stretchy":839},[837,2909,1374],{},[595,2911,1378],{"mathvariant":1377},[599,2913,2914],{"encoding":601},"f(x) \\to \\infty",[576,2916,2918,2945],{"className":2917,"ariaHidden":606},[605],[576,2919,2921,2924,2927,2930,2933,2936,2939,2942],{"className":2920},[610],[576,2922],{"className":2923,"style":867},[614],[576,2925,835],{"className":2926,"style":871},[619,620],[576,2928,840],{"className":2929},[875],[576,2931,1117],{"className":2932},[619,620],[576,2934,845],{"className":2935},[882],[576,2937],{"className":2938,"style":887},[886],[576,2940,1374],{"className":2941},[891],[576,2943],{"className":2944,"style":887},[886],[576,2946,2948,2951],{"className":2947},[610],[576,2949],{"className":2950,"style":615},[614],[576,2952,1378],{"className":2953},[619],". Zur Kontrolle: ",[576,2956,2958,2999],{"className":2957},[579],[576,2959,2961],{"className":2960},[583],[585,2962,2963],{"xmlns":587},[589,2964,2965,2996],{},[592,2966,2967,2969,2971,2973,2976,2978,2980,2982,2984,2988,2991,2993],{},[595,2968,835],{},[837,2970,840],{"stretchy":839},[837,2972,1048],{},[635,2974,2975],{},"100",[837,2977,845],{"stretchy":839},[837,2979,848],{},[837,2981,1048],{},[635,2983,795],{},[2985,2986,2987],"mtext",{}," ",[635,2989,2990],{},"039",[2985,2992,2987],{},[635,2994,2995],{},"400",[599,2997,2998],{"encoding":601},"f(-100) = -2\\,039\\,400",[576,3000,3002,3032],{"className":3001,"ariaHidden":606},[605],[576,3003,3005,3008,3011,3014,3017,3020,3023,3026,3029],{"className":3004},[610],[576,3006],{"className":3007,"style":867},[614],[576,3009,835],{"className":3010,"style":871},[619,620],[576,3012,840],{"className":3013},[875],[576,3015,1048],{"className":3016},[619],[576,3018,2975],{"className":3019},[619],[576,3021,845],{"className":3022},[882],[576,3024],{"className":3025,"style":887},[886],[576,3027,848],{"className":3028},[891],[576,3030],{"className":3031,"style":887},[886],[576,3033,3035,3038,3041,3044,3047,3050,3053],{"className":3034},[610],[576,3036],{"className":3037,"style":2176},[614],[576,3039,1048],{"className":3040},[619],[576,3042,795],{"className":3043},[619],[576,3045],{"className":3046,"style":1928},[886],[576,3048,2990],{"className":3049},[619],[576,3051],{"className":3052,"style":1928},[886],[576,3054,2995],{"className":3055},[619],[576,3057,3059,3092],{"className":3058},[579],[576,3060,3062],{"className":3061},[583],[585,3063,3064],{"xmlns":587},[589,3065,3066,3089],{},[592,3067,3068,3070,3072,3074,3076,3078,3080,3082,3085,3087],{},[595,3069,835],{},[837,3071,840],{"stretchy":839},[635,3073,2975],{},[837,3075,845],{"stretchy":839},[837,3077,848],{},[635,3079,765],{},[2985,3081,2987],{},[635,3083,3084],{},"959",[2985,3086,2987],{},[635,3088,2995],{},[599,3090,3091],{"encoding":601},"f(100) = 1\\,959\\,400",[576,3093,3095,3122],{"className":3094,"ariaHidden":606},[605],[576,3096,3098,3101,3104,3107,3110,3113,3116,3119],{"className":3097},[610],[576,3099],{"className":3100,"style":867},[614],[576,3102,835],{"className":3103,"style":871},[619,620],[576,3105,840],{"className":3106},[875],[576,3108,2975],{"className":3109},[619],[576,3111,845],{"className":3112},[882],[576,3114],{"className":3115,"style":887},[886],[576,3117,848],{"className":3118},[891],[576,3120],{"className":3121,"style":887},[886],[576,3123,3125,3128,3131,3134,3137,3140],{"className":3124},[610],[576,3126],{"className":3127,"style":649},[614],[576,3129,765],{"className":3130},[619],[576,3132],{"className":3133,"style":1928},[886],[576,3135,3084],{"className":3136},[619],[576,3138],{"className":3139,"style":1928},[886],[576,3141,2995],{"className":3142},[619],[559,3144,3146],{"id":3145},"typische-fehler","Typische Fehler",[815,3148,3149,3333,3505],{},[818,3150,3151,3152,1612,3275,3303,3304,3332],{},"Den Grad am ersten Summanden ablesen: ",[576,3153,3155,3189],{"className":3154},[579],[576,3156,3158],{"className":3157},[583],[585,3159,3160],{"xmlns":587},[589,3161,3162,3186],{},[592,3163,3164,3166,3168,3170,3172,3174,3176,3178,3180],{},[595,3165,835],{},[837,3167,840],{"stretchy":839},[595,3169,1117],{},[837,3171,845],{"stretchy":839},[837,3173,848],{},[635,3175,1452],{},[595,3177,1117],{},[837,3179,1874],{},[1113,3181,3182,3184],{},[595,3183,1117],{},[635,3185,1457],{},[599,3187,3188],{"encoding":601},"f(x) = 3x + x^4",[576,3190,3192,3219,3240],{"className":3191,"ariaHidden":606},[605],[576,3193,3195,3198,3201,3204,3207,3210,3213,3216],{"className":3194},[610],[576,3196],{"className":3197,"style":867},[614],[576,3199,835],{"className":3200,"style":871},[619,620],[576,3202,840],{"className":3203},[875],[576,3205,1117],{"className":3206},[619,620],[576,3208,845],{"className":3209},[882],[576,3211],{"className":3212,"style":887},[886],[576,3214,848],{"className":3215},[891],[576,3217],{"className":3218,"style":887},[886],[576,3220,3222,3225,3228,3231,3234,3237],{"className":3221},[610],[576,3223],{"className":3224,"style":2176},[614],[576,3226,1452],{"className":3227},[619],[576,3229,1117],{"className":3230},[619,620],[576,3232],{"className":3233,"style":1070},[886],[576,3235,1874],{"className":3236},[1074],[576,3238],{"className":3239,"style":1070},[886],[576,3241,3243,3246],{"className":3242},[610],[576,3244],{"className":3245,"style":1532},[614],[576,3247,3249,3252],{"className":3248},[619],[576,3250,1117],{"className":3251},[619,620],[576,3253,3255],{"className":3254},[700],[576,3256,3258],{"className":3257},[704],[576,3259,3261],{"className":3260},[709],[576,3262,3264],{"className":3263,"style":1532},[713],[576,3265,3266,3269],{"style":1194},[576,3267],{"className":3268,"style":722},[721],[576,3270,3272],{"className":3271},[726,727,728,729],[576,3273,1457],{"className":3274},[619,729],[576,3276,3278,3291],{"className":3277},[579],[576,3279,3281],{"className":3280},[583],[585,3282,3283],{"xmlns":587},[589,3284,3285,3289],{},[592,3286,3287],{},[635,3288,1457],{},[599,3290,1457],{"encoding":601},[576,3292,3294],{"className":3293,"ariaHidden":606},[605],[576,3295,3297,3300],{"className":3296},[610],[576,3298],{"className":3299,"style":649},[614],[576,3301,1457],{"className":3302},[619],", nicht ",[576,3305,3307,3320],{"className":3306},[579],[576,3308,3310],{"className":3309},[583],[585,3311,3312],{"xmlns":587},[589,3313,3314,3318],{},[592,3315,3316],{},[635,3317,765],{},[599,3319,765],{"encoding":601},[576,3321,3323],{"className":3322,"ariaHidden":606},[605],[576,3324,3326,3329],{"className":3325},[610],[576,3327],{"className":3328,"style":649},[614],[576,3330,765],{"className":3331},[619],". Maßgeblich ist der höchste Exponent.",[818,3334,3335,3336,3364,3365,3393,3394,3475,3476,3504],{},"Glauben, dass eine Funktion vom Grad ",[576,3337,3339,3352],{"className":3338},[579],[576,3340,3342],{"className":3341},[583],[585,3343,3344],{"xmlns":587},[589,3345,3346,3350],{},[592,3347,3348],{},[595,3349,597],{},[599,3351,597],{"encoding":601},[576,3353,3355],{"className":3354,"ariaHidden":606},[605],[576,3356,3358,3361],{"className":3357},[610],[576,3359],{"className":3360,"style":615},[614],[576,3362,597],{"className":3363},[619,620]," immer genau ",[576,3366,3368,3381],{"className":3367},[579],[576,3369,3371],{"className":3370},[583],[585,3372,3373],{"xmlns":587},[589,3374,3375,3379],{},[592,3376,3377],{},[595,3378,597],{},[599,3380,597],{"encoding":601},[576,3382,3384],{"className":3383,"ariaHidden":606},[605],[576,3385,3387,3390],{"className":3386},[610],[576,3388],{"className":3389,"style":615},[614],[576,3391,597],{"className":3392},[619,620]," Nullstellen hat: ",[576,3395,3397,3419],{"className":3396},[579],[576,3398,3400],{"className":3399},[583],[585,3401,3402],{"xmlns":587},[589,3403,3404,3416],{},[592,3405,3406,3412,3414],{},[1113,3407,3408,3410],{},[595,3409,1117],{},[635,3411,795],{},[837,3413,1874],{},[635,3415,765],{},[599,3417,3418],{"encoding":601},"x^2 + 1",[576,3420,3422,3466],{"className":3421,"ariaHidden":606},[605],[576,3423,3425,3428,3457,3460,3463],{"className":3424},[610],[576,3426],{"className":3427,"style":1510},[614],[576,3429,3431,3434],{"className":3430},[619],[576,3432,1117],{"className":3433},[619,620],[576,3435,3437],{"className":3436},[700],[576,3438,3440],{"className":3439},[704],[576,3441,3443],{"className":3442},[709],[576,3444,3446],{"className":3445,"style":1532},[713],[576,3447,3448,3451],{"style":1194},[576,3449],{"className":3450,"style":722},[721],[576,3452,3454],{"className":3453},[726,727,728,729],[576,3455,795],{"className":3456},[619,729],[576,3458],{"className":3459,"style":1070},[886],[576,3461,1874],{"className":3462},[1074],[576,3464],{"className":3465,"style":1070},[886],[576,3467,3469,3472],{"className":3468},[610],[576,3470],{"className":3471,"style":649},[614],[576,3473,765],{"className":3474},[619]," ist nie kleiner als ",[576,3477,3479,3492],{"className":3478},[579],[576,3480,3482],{"className":3481},[583],[585,3483,3484],{"xmlns":587},[589,3485,3486,3490],{},[592,3487,3488],{},[635,3489,765],{},[599,3491,765],{"encoding":601},[576,3493,3495],{"className":3494,"ariaHidden":606},[605],[576,3496,3498,3501],{"className":3497},[610],[576,3499],{"className":3500,"style":649},[614],[576,3502,765],{"className":3503},[619]," und hat deshalb keine reelle Nullstelle.",[818,3506,3507,3508,3577,3578,3642],{},"Beim Verhalten im Unendlichen das Vorzeichen von ",[576,3509,3511,3528],{"className":3510},[579],[576,3512,3514],{"className":3513},[583],[585,3515,3516],{"xmlns":587},[589,3517,3518,3526],{},[592,3519,3520],{},[671,3521,3522,3524],{},[595,3523,675],{},[595,3525,597],{},[599,3527,680],{"encoding":601},[576,3529,3531],{"className":3530,"ariaHidden":606},[605],[576,3532,3534,3537],{"className":3533},[610],[576,3535],{"className":3536,"style":690},[614],[576,3538,3540,3543],{"className":3539},[619],[576,3541,675],{"className":3542},[619,620],[576,3544,3546],{"className":3545},[700],[576,3547,3549,3569],{"className":3548},[704,705],[576,3550,3552,3566],{"className":3551},[709],[576,3553,3555],{"className":3554,"style":714},[713],[576,3556,3557,3560],{"style":717},[576,3558],{"className":3559,"style":722},[721],[576,3561,3563],{"className":3562},[726,727,728,729],[576,3564,597],{"className":3565},[619,620,729],[576,3567,737],{"className":3568},[736],[576,3570,3572],{"className":3571},[709],[576,3573,3575],{"className":3574,"style":744},[713],[576,3576],{}," übersehen: ",[576,3579,3581,3601],{"className":3580},[579],[576,3582,3584],{"className":3583},[583],[585,3585,3586],{"xmlns":587},[589,3587,3588,3598],{},[592,3589,3590,3592],{},[837,3591,1048],{},[1113,3593,3594,3596],{},[595,3595,1117],{},[635,3597,1457],{},[599,3599,3600],{"encoding":601},"-x^4",[576,3602,3604],{"className":3603,"ariaHidden":606},[605],[576,3605,3607,3610,3613],{"className":3606},[610],[576,3608],{"className":3609,"style":1510},[614],[576,3611,1048],{"className":3612},[619],[576,3614,3616,3619],{"className":3615},[619],[576,3617,1117],{"className":3618},[619,620],[576,3620,3622],{"className":3621},[700],[576,3623,3625],{"className":3624},[704],[576,3626,3628],{"className":3627},[709],[576,3629,3631],{"className":3630,"style":1532},[713],[576,3632,3633,3636],{"style":1194},[576,3634],{"className":3635,"style":722},[721],[576,3637,3639],{"className":3638},[726,727,728,729],[576,3640,1457],{"className":3641},[619,729]," geht an beiden Enden nach unten.",{"title":3644,"searchDepth":3645,"depth":3645,"links":3646},"",2,[3647,3648,3649],{"id":561,"depth":3645,"text":562},{"id":1418,"depth":3645,"text":1419},{"id":3145,"depth":3645,"text":3146},[3651,3654,3657,3659,3662,3665,3668,3671,3673,3677,3681],{"lhs":3652,"rhs":3653},"a3*0^3 + a2*0^2 + a1*0 + a0","a0",{"lhs":3655,"rhs":3656},"2*x^3 - 4*x^2 - 6*x","2*x*(x^2 - 2*x - 3)",{"lhs":3656,"rhs":3658},"2*x*(x - 3)*(x + 1)",{"lhs":3655,"rhs":637,"where":3660},{"x":3661},0,{"lhs":3655,"rhs":637,"where":3663},{"x":3664},3,{"lhs":3655,"rhs":637,"where":3666},{"x":3667},-1,{"lhs":3655,"rhs":3669,"where":3670},"-12",{"x":3645},{"lhs":3672,"rhs":3669},"16 - 16 - 12",{"lhs":3655,"rhs":3674,"where":3675},"-2039400",{"x":3676},-100,{"lhs":3655,"rhs":3678,"where":3679},"1959400",{"x":3680},100,{"lhs":3418,"rhs":765,"where":3682},{"x":3661},"n \\in \\mathbb{N}_0,\\ a_0, \\ldots, a_n \\in \\mathbb{R},\\ a_n \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsub>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N}_0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_0, \\ldots, a_n \\in \\mathbb{R},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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