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Der Quotient hat einen Grad weniger. So wird aus einer Gleichung dritten Grades eine quadratische Gleichung.",[563,1059,1060],{},"Ablauf in jedem Schritt:",[1062,1063,1064,1068,1071,1077],"ol",{},[1065,1066,1067],"li",{},"Den höchsten Term des Dividenden durch den höchsten Term des Divisors teilen. Das ergibt den nächsten Term des Ergebnisses.",[1065,1069,1070],{},"Diesen Term mit dem ganzen Divisor multiplizieren.",[1065,1072,1073,1074,822],{},"Das Produkt vom Dividenden ",[567,1075,1076],{},"abziehen",[1065,1078,1079],{},"Mit dem Rest weitermachen, bis sein Grad kleiner ist als der des Divisors.",[563,1081,1082,1083,1112,1113,822],{},"Fehlende Potenzen schreibt man vorher mit ",[571,1084,1086,1099],{"className":1085},[574],[571,1087,1089],{"className":1088},[578],[580,1090,1091],{"xmlns":582},[584,1092,1093,1097],{},[587,1094,1095],{},[844,1096,846],{},[604,1098,846],{"encoding":606},[571,1100,1102],{"className":1101,"ariaHidden":612},[611],[571,1103,1105,1109],{"className":1104},[616],[571,1106],{"className":1107,"style":1108},[620],"height:0.6444em;",[571,1110,846],{"className":1111},[625]," dazu, z.B. ",[571,1114,1116,1161],{"className":1115},[574],[571,1117,1119],{"className":1118},[578],[580,1120,1121],{"xmlns":582},[584,1122,1123,1158],{},[587,1124,1125,1128,1136,1139,1141,1147,1149,1151,1153,1155],{},[844,1126,1127],{},"2",[1129,1130,1131,1133],"msup",{},[590,1132,599],{},[844,1134,1135],{},"3",[593,1137,1138],{},"+",[844,1140,1135],{},[1129,1142,1143,1145],{},[590,1144,599],{},[844,1146,1127],{},[593,1148,1138],{},[844,1150,846],{},[590,1152,599],{},[593,1154,965],{},[844,1156,1157],{},"1",[604,1159,1160],{"encoding":606},"2x^3 + 3x^2 + 0x - 1",[571,1162,1164,1214,1261,1283],{"className":1163,"ariaHidden":612},[611],[571,1165,1167,1171,1174,1205,1208,1211],{"className":1166},[616],[571,1168],{"className":1169,"style":1170},[620],"height:0.8974em;vertical-align:-0.0833em;",[571,1172,1127],{"className":1173},[625],[571,1175,1177,1180],{"className":1176},[625],[571,1178,599],{"className":1179},[625,626],[571,1181,1183],{"className":1182},[869],[571,1184,1186],{"className":1185},[873],[571,1187,1189],{"className":1188},[878],[571,1190,1193],{"className":1191,"style":1192},[882],"height:0.8141em;",[571,1194,1196,1199],{"style":1195},"top:-3.063em;margin-right:0.05em;",[571,1197],{"className":1198,"style":891},[890],[571,1200,1202],{"className":1201},[895,896,897,898],[571,1203,1135],{"className":1204},[625,898],[571,1206],{"className":1207,"style":996},[995],[571,1209,1138],{"className":1210},[1000],[571,1212],{"className":1213,"style":996},[995],[571,1215,1217,1220,1223,1252,1255,1258],{"className":1216},[616],[571,1218],{"className":1219,"style":1170},[620],[571,1221,1135],{"className":1222},[625],[571,1224,1226,1229],{"className":1225},[625],[571,1227,599],{"className":1228},[625,626],[571,1230,1232],{"className":1231},[869],[571,1233,1235],{"className":1234},[873],[571,1236,1238],{"className":1237},[878],[571,1239,1241],{"className":1240,"style":1192},[882],[571,1242,1243,1246],{"style":1195},[571,1244],{"className":1245,"style":891},[890],[571,1247,1249],{"className":1248},[895,896,897,898],[571,1250,1127],{"className":1251},[625,898],[571,1253],{"className":1254,"style":996},[995],[571,1256,1138],{"className":1257},[1000],[571,1259],{"className":1260,"style":996},[995],[571,1262,1264,1268,1271,1274,1277,1280],{"className":1263},[616],[571,1265],{"className":1266,"style":1267},[620],"height:0.7278em;vertical-align:-0.0833em;",[571,1269,846],{"className":1270},[625],[571,1272,599],{"className":1273},[625,626],[571,1275],{"className":1276,"style":996},[995],[571,1278,965],{"className":1279},[1000],[571,1281],{"className":1282,"style":996},[995],[571,1284,1286,1289],{"className":1285},[616],[571,1287],{"className":1288,"style":1108},[620],[571,1290,1157],{"className":1291},[625],[558,1293,1295],{"id":1294},"beispiele","Beispiele",[563,1297,1298,1505,1506,1558,1559,1676,1677,1738],{},[571,1299,1301,1352],{"className":1300},[574],[571,1302,1304],{"className":1303},[578],[580,1305,1306],{"xmlns":582},[584,1307,1308,1349],{},[587,1309,1310,1312,1314,1316,1318,1321,1327,1329,1331,1337,1339,1342,1344,1346],{},[590,1311,563],{},[593,1313,596],{"stretchy":595},[590,1315,599],{},[593,1317,602],{"stretchy":595},[593,1319,1320],{},"=",[1129,1322,1323,1325],{},[590,1324,599],{},[844,1326,1135],{},[593,1328,965],{},[844,1330,1127],{},[1129,1332,1333,1335],{},[590,1334,599],{},[844,1336,1127],{},[593,1338,965],{},[844,1340,1341],{},"5",[590,1343,599],{},[593,1345,1138],{},[844,1347,1348],{},"6",[604,1350,1351],{"encoding":606},"p(x) = x^3 - 2x^2 - 5x + 6",[571,1353,1355,1384,1428,1475,1496],{"className":1354,"ariaHidden":612},[611],[571,1356,1358,1361,1364,1367,1370,1373,1377,1381],{"className":1357},[616],[571,1359],{"className":1360,"style":621},[620],[571,1362,563],{"className":1363},[625,626],[571,1365,596],{"className":1366},[630],[571,1368,599],{"className":1369},[625,626],[571,1371,602],{"className":1372},[637],[571,1374],{"className":1375,"style":1376},[995],"margin-right:0.2778em;",[571,1378,1320],{"className":1379},[1380],"mrel",[571,1382],{"className":1383,"style":1376},[995],[571,1385,1387,1390,1419,1422,1425],{"className":1386},[616],[571,1388],{"className":1389,"style":1170},[620],[571,1391,1393,1396],{"className":1392},[625],[571,1394,599],{"className":1395},[625,626],[571,1397,1399],{"className":1398},[869],[571,1400,1402],{"className":1401},[873],[571,1403,1405],{"className":1404},[878],[571,1406,1408],{"className":1407,"style":1192},[882],[571,1409,1410,1413],{"style":1195},[571,1411],{"className":1412,"style":891},[890],[571,1414,1416],{"className":1415},[895,896,897,898],[571,1417,1135],{"className":1418},[625,898],[571,1420],{"className":1421,"style":996},[995],[571,1423,965],{"className":1424},[1000],[571,1426],{"className":1427,"style":996},[995],[571,1429,1431,1434,1437,1466,1469,1472],{"className":1430},[616],[571,1432],{"className":1433,"style":1170},[620],[571,1435,1127],{"className":1436},[625],[571,1438,1440,1443],{"className":1439},[625],[571,1441,599],{"className":1442},[625,626],[571,1444,1446],{"className":1445},[869],[571,1447,1449],{"className":1448},[873],[571,1450,1452],{"className":1451},[878],[571,1453,1455],{"className":1454,"style":1192},[882],[571,1456,1457,1460],{"style":1195},[571,1458],{"className":1459,"style":891},[890],[571,1461,1463],{"className":1462},[895,896,897,898],[571,1464,1127],{"className":1465},[625,898],[571,1467],{"className":1468,"style":996},[995],[571,1470,965],{"className":1471},[1000],[571,1473],{"className":1474,"style":996},[995],[571,1476,1478,1481,1484,1487,1490,1493],{"className":1477},[616],[571,1479],{"className":1480,"style":1267},[620],[571,1482,1341],{"className":1483},[625],[571,1485,599],{"className":1486},[625,626],[571,1488],{"className":1489,"style":996},[995],[571,1491,1138],{"className":1492},[1000],[571,1494],{"className":1495,"style":996},[995],[571,1497,1499,1502],{"className":1498},[616],[571,1500],{"className":1501,"style":1108},[620],[571,1503,1348],{"className":1504},[625]," hat die Nullstelle ",[571,1507,1509,1527],{"className":1508},[574],[571,1510,1512],{"className":1511},[578],[580,1513,1514],{"xmlns":582},[584,1515,1516,1524],{},[587,1517,1518,1520,1522],{},[590,1519,599],{},[593,1521,1320],{},[844,1523,1157],{},[604,1525,1526],{"encoding":606},"x = 1",[571,1528,1530,1549],{"className":1529,"ariaHidden":612},[611],[571,1531,1533,1537,1540,1543,1546],{"className":1532},[616],[571,1534],{"className":1535,"style":1536},[620],"height:0.4306em;",[571,1538,599],{"className":1539},[625,626],[571,1541],{"className":1542,"style":1376},[995],[571,1544,1320],{"className":1545},[1380],[571,1547],{"className":1548,"style":1376},[995],[571,1550,1552,1555],{"className":1551},[616],[571,1553],{"className":1554,"style":1108},[620],[571,1556,1157],{"className":1557},[625],", denn ",[571,1560,1562,1592],{"className":1561},[574],[571,1563,1565],{"className":1564},[578],[580,1566,1567],{"xmlns":582},[584,1568,1569,1589],{},[587,1570,1571,1573,1575,1577,1579,1581,1583,1585,1587],{},[844,1572,1157],{},[593,1574,965],{},[844,1576,1127],{},[593,1578,965],{},[844,1580,1341],{},[593,1582,1138],{},[844,1584,1348],{},[593,1586,1320],{},[844,1588,846],{},[604,1590,1591],{"encoding":606},"1 - 2 - 5 + 6 = 0",[571,1593,1595,1613,1631,1649,1667],{"className":1594,"ariaHidden":612},[611],[571,1596,1598,1601,1604,1607,1610],{"className":1597},[616],[571,1599],{"className":1600,"style":1267},[620],[571,1602,1157],{"className":1603},[625],[571,1605],{"className":1606,"style":996},[995],[571,1608,965],{"className":1609},[1000],[571,1611],{"className":1612,"style":996},[995],[571,1614,1616,1619,1622,1625,1628],{"className":1615},[616],[571,1617],{"className":1618,"style":1267},[620],[571,1620,1127],{"className":1621},[625],[571,1623],{"className":1624,"style":996},[995],[571,1626,965],{"className":1627},[1000],[571,1629],{"className":1630,"style":996},[995],[571,1632,1634,1637,1640,1643,1646],{"className":1633},[616],[571,1635],{"className":1636,"style":1267},[620],[571,1638,1341],{"className":1639},[625],[571,1641],{"className":1642,"style":996},[995],[571,1644,1138],{"className":1645},[1000],[571,1647],{"className":1648,"style":996},[995],[571,1650,1652,1655,1658,1661,1664],{"className":1651},[616],[571,1653],{"className":1654,"style":1108},[620],[571,1656,1348],{"className":1657},[625],[571,1659],{"className":1660,"style":1376},[995],[571,1662,1320],{"className":1663},[1380],[571,1665],{"className":1666,"style":1376},[995],[571,1668,1670,1673],{"className":1669},[616],[571,1671],{"className":1672,"style":1108},[620],[571,1674,846],{"className":1675},[625],". Division durch ",[571,1678,1680,1702],{"className":1679},[574],[571,1681,1683],{"className":1682},[578],[580,1684,1685],{"xmlns":582},[584,1686,1687,1699],{},[587,1688,1689,1691,1693,1695,1697],{},[593,1690,596],{"stretchy":595},[590,1692,599],{},[593,1694,965],{},[844,1696,1157],{},[593,1698,602],{"stretchy":595},[604,1700,1701],{"encoding":606},"(x - 1)",[571,1703,1705,1726],{"className":1704,"ariaHidden":612},[611],[571,1706,1708,1711,1714,1717,1720,1723],{"className":1707},[616],[571,1709],{"className":1710,"style":621},[620],[571,1712,596],{"className":1713},[630],[571,1715,599],{"className":1716},[625,626],[571,1718],{"className":1719,"style":996},[995],[571,1721,965],{"className":1722},[1000],[571,1724],{"className":1725,"style":996},[995],[571,1727,1729,1732,1735],{"className":1728},[616],[571,1730],{"className":1731,"style":621},[620],[571,1733,1157],{"className":1734},[625],[571,1736,602],{"className":1737},[637],":",[571,1740,1743],{"className":1741},[1742],"katex-display",[571,1744,1746,2087],{"className":1745},[574],[571,1747,1749],{"className":1748},[578],[580,1750,1752],{"xmlns":582,"display":1751},"block",[584,1753,1754,2084],{},[1755,1756,1760,1884,1990],"mtable",{"rowspacing":1757,"columnalign":1758,"columnspacing":1759},"0.25em","right left right left right left","0em 1em 0em 1em 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: x = x^2, && x^2 (x - 1) = x^3 - x^2, && \\text{Rest: } -x^2 - 5x + 6 \\\\\n&-x^2 : x = -x, && -x(x - 1) = -x^2 + x, && \\text{Rest: } -6x + 6 \\\\\n&-6x : x = -6, && -6(x - 1) = -6x + 6, && \\text{Rest: } 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6",[571,3105,3107,3155,3202,3223,3244,3265,3286,3330,3349],{"className":3106,"ariaHidden":612},[611],[571,3108,3110,3114,3117,3146,3149,3152],{"className":3109},[616],[571,3111],{"className":3112,"style":3113},[620],"height:1.0641em;vertical-align:-0.25em;",[571,3115,596],{"className":3116},[630],[571,3118,3120,3123],{"className":3119},[625],[571,3121,599],{"className":3122},[625,626],[571,3124,3126],{"className":3125},[869],[571,3127,3129],{"className":3128},[873],[571,3130,3132],{"className":3131},[878],[571,3133,3135],{"className":3134,"style":1192},[882],[571,3136,3137,3140],{"style":1195},[571,3138],{"className":3139,"style":891},[890],[571,3141,3143],{"className":3142},[895,896,897,898],[571,3144,1135],{"className":3145},[625,898],[571,3147],{"className":3148,"style":996},[995],[571,3150,965],{"className":3151},[1000],[571,3153],{"className":3154,"style":996},[995],[571,3156,3158,3161,3164,3193,3196,3199],{"className":3157},[616],[571,3159],{"className":3160,"style":1170},[620],[571,3162,1127],{"className":3163},[625],[571,3165,3167,3170],{"className":3166},[625],[571,3168,599],{"className":3169},[625,626],[571,3171,3173],{"className":3172},[869],[571,3174,3176],{"className":3175},[873],[571,3177,3179],{"className":3178},[878],[571,3180,3182],{"className":3181,"style":1192},[882],[571,3183,3184,3187],{"style":1195},[571,3185],{"className":3186,"style":891},[890],[571,3188,3190],{"className":3189},[895,896,897,898],[571,3191,1127],{"className":3192},[625,898],[571,3194],{"className":3195,"style":996},[995],[571,3197,965],{"className":3198},[1000],[571,3200],{"className":3201,"style":996},[995],[571,3203,3205,3208,3211,3214,3217,3220],{"className":3204},[616],[571,3206],{"className":3207,"style":1267},[620],[571,3209,1341],{"className":3210},[625],[571,3212,599],{"className":3213},[625,626],[571,3215],{"className":3216,"style":996},[995],[571,3218,1138],{"className":3219},[1000],[571,3221],{"className":3222,"style":996},[995],[571,3224,3226,3229,3232,3235,3238,3241],{"className":3225},[616],[571,3227],{"className":3228,"style":621},[620],[571,3230,1348],{"className":3231},[625],[571,3233,602],{"className":3234},[637],[571,3236],{"className":3237,"style":1376},[995],[571,3239,1738],{"className":3240},[1380],[571,3242],{"className":3243,"style":1376},[995],[571,3245,3247,3250,3253,3256,3259,3262],{"className":3246},[616],[571,3248],{"className":3249,"style":621},[620],[571,3251,596],{"className":3252},[630],[571,3254,599],{"className":3255},[625,626],[571,3257],{"className":3258,"style":996},[995],[571,3260,965],{"className":3261},[1000],[571,3263],{"className":3264,"style":996},[995],[571,3266,3268,3271,3274,3277,3280,3283],{"className":3267},[616],[571,3269],{"className":3270,"style":621},[620],[571,3272,1157],{"className":3273},[625],[571,3275,602],{"className":3276},[637],[571,3278],{"className":3279,"style":1376},[995],[571,3281,1320],{"className":3282},[1380],[571,3284],{"className":3285,"style":1376},[995],[571,3287,3289,3292,3321,3324,3327],{"className":3288},[616],[571,3290],{"className":3291,"style":1170},[620],[571,3293,3295,3298],{"className":3294},[625],[571,3296,599],{"className":3297},[625,626],[571,3299,3301],{"className":3300},[869],[571,3302,3304],{"className":3303},[873],[571,3305,3307],{"className":3306},[878],[571,3308,3310],{"className":3309,"style":1192},[882],[571,3311,3312,3315],{"style":1195},[571,3313],{"className":3314,"style":891},[890],[571,3316,3318],{"className":3317},[895,896,897,898],[571,3319,1127],{"className":3320},[625,898],[571,3322],{"className":3323,"style":996},[995],[571,3325,965],{"className":3326},[1000],[571,3328],{"className":3329,"style":996},[995],[571,3331,3333,3337,3340,3343,3346],{"className":3332},[616],[571,3334],{"className":3335,"style":3336},[620],"height:0.6667em;vertical-align:-0.0833em;",[571,3338,599],{"className":3339},[625,626],[571,3341],{"className":3342,"style":996},[995],[571,3344,965],{"className":3345},[1000],[571,3347],{"className":3348,"style":996},[995],[571,3350,3352,3355],{"className":3351},[616],[571,3353],{"className":3354,"style":1108},[620],[571,3356,1348],{"className":3357},[625],". Die quadratische Gleichung ",[571,3360,3362,3392],{"className":3361},[574],[571,3363,3365],{"className":3364},[578],[580,3366,3367],{"xmlns":582},[584,3368,3369,3389],{},[587,3370,3371,3377,3379,3381,3383,3385,3387],{},[1129,3372,3373,3375],{},[590,3374,599],{},[844,3376,1127],{},[593,3378,965],{},[590,3380,599],{},[593,3382,965],{},[844,3384,1348],{},[593,3386,1320],{},[844,3388,846],{},[604,3390,3391],{"encoding":606},"x^2 - x - 6 = 0",[571,3393,3395,3439,3457,3475],{"className":3394,"ariaHidden":612},[611],[571,3396,3398,3401,3430,3433,3436],{"className":3397},[616],[571,3399],{"className":3400,"style":1170},[620],[571,3402,3404,3407],{"className":3403},[625],[571,3405,599],{"className":3406},[625,626],[571,3408,3410],{"className":3409},[869],[571,3411,3413],{"className":3412},[873],[571,3414,3416],{"className":3415},[878],[571,3417,3419],{"className":3418,"style":1192},[882],[571,3420,3421,3424],{"style":1195},[571,3422],{"className":3423,"style":891},[890],[571,3425,3427],{"className":3426},[895,896,897,898],[571,3428,1127],{"className":3429},[625,898],[571,3431],{"className":3432,"style":996},[995],[571,3434,965],{"className":3435},[1000],[571,3437],{"className":3438,"style":996},[995],[571,3440,3442,3445,3448,3451,3454],{"className":3441},[616],[571,3443],{"className":3444,"style":3336},[620],[571,3446,599],{"className":3447},[625,626],[571,3449],{"className":3450,"style":996},[995],[571,3452,965],{"className":3453},[1000],[571,3455],{"className":3456,"style":996},[995],[571,3458,3460,3463,3466,3469,3472],{"className":3459},[616],[571,3461],{"className":3462,"style":1108},[620],[571,3464,1348],{"className":3465},[625],[571,3467],{"className":3468,"style":1376},[995],[571,3470,1320],{"className":3471},[1380],[571,3473],{"className":3474,"style":1376},[995],[571,3476,3478,3481],{"className":3477},[616],[571,3479],{"className":3480,"style":1108},[620],[571,3482,846],{"className":3483},[625]," liefert die weiteren Nullstellen:",[571,3486,3488],{"className":3487},[1742],[571,3489,3491,3561],{"className":3490},[574],[571,3492,3494],{"className":3493},[578],[580,3495,3496],{"xmlns":582,"display":1751},[584,3497,3498,3558],{},[587,3499,3500,3506,3508,3510,3516,3518,3520,3522,3524,3526,3528,3530,3532,3534,3536,3538,3540,3542,3544,3546,3548,3550,3552,3554,3556],{},[1129,3501,3502,3504],{},[590,3503,599],{},[844,3505,1135],{},[593,3507,965],{},[844,3509,1127],{},[1129,3511,3512,3514],{},[590,3513,599],{},[844,3515,1127],{},[593,3517,965],{},[844,3519,1341],{},[590,3521,599],{},[593,3523,1138],{},[844,3525,1348],{},[593,3527,1320],{},[593,3529,596],{"stretchy":595},[590,3531,599],{},[593,3533,965],{},[844,3535,1157],{},[593,3537,602],{"stretchy":595},[593,3539,596],{"stretchy":595},[590,3541,599],{},[593,3543,965],{},[844,3545,1135],{},[593,3547,602],{"stretchy":595},[593,3549,596],{"stretchy":595},[590,3551,599],{},[593,3553,1138],{},[844,3555,1127],{},[593,3557,602],{"stretchy":595},[604,3559,3560],{"encoding":606},"x^3 - 2x^2 - 5x + 6 = (x - 1)(x - 3)(x + 2)",[571,3562,3564,3609,3656,3677,3695,3716,3743,3770],{"className":3563,"ariaHidden":612},[611],[571,3565,3567,3571,3600,3603,3606],{"className":3566},[616],[571,3568],{"className":3569,"style":3570},[620],"height:0.9474em;vertical-align:-0.0833em;",[571,3572,3574,3577],{"className":3573},[625],[571,3575,599],{"className":3576},[625,626],[571,3578,3580],{"className":3579},[869],[571,3581,3583],{"className":3582},[873],[571,3584,3586],{"className":3585},[878],[571,3587,3589],{"className":3588,"style":2201},[882],[571,3590,3591,3594],{"style":2204},[571,3592],{"className":3593,"style":891},[890],[571,3595,3597],{"className":3596},[895,896,897,898],[571,3598,1135],{"className":3599},[625,898],[571,3601],{"className":3602,"style":996},[995],[571,3604,965],{"className":3605},[1000],[571,3607],{"className":3608,"style":996},[995],[571,3610,3612,3615,3618,3647,3650,3653],{"className":3611},[616],[571,3613],{"className":3614,"style":3570},[620],[571,3616,1127],{"className":3617},[625],[571,3619,3621,3624],{"className":3620},[625],[571,3622,599],{"className":3623},[625,626],[571,3625,3627],{"className":3626},[869],[571,3628,3630],{"className":3629},[873],[571,3631,3633],{"className":3632},[878],[571,3634,3636],{"className":3635,"style":2201},[882],[571,3637,3638,3641],{"style":2204},[571,3639],{"className":3640,"style":891},[890],[571,3642,3644],{"className":3643},[895,896,897,898],[571,3645,1127],{"className":3646},[625,898],[571,3648],{"className":3649,"style":996},[995],[571,3651,965],{"className":3652},[1000],[571,3654],{"className":3655,"style":996},[995],[571,3657,3659,3662,3665,3668,3671,3674],{"className":3658},[616],[571,3660],{"className":3661,"style":1267},[620],[571,3663,1341],{"className":3664},[625],[571,3666,599],{"className":3667},[625,626],[571,3669],{"className":3670,"style":996},[995],[571,3672,1138],{"className":3673},[1000],[571,3675],{"className":3676,"style":996},[995],[571,3678,3680,3683,3686,3689,3692],{"className":3679},[616],[571,3681],{"className":3682,"style":1108},[620],[571,3684,1348],{"className":3685},[625],[571,3687],{"className":3688,"style":1376},[995],[571,3690,1320],{"className":3691},[1380],[571,3693],{"className":3694,"style":1376},[995],[571,3696,3698,3701,3704,3707,3710,3713],{"className":3697},[616],[571,3699],{"className":3700,"style":621},[620],[571,3702,596],{"className":3703},[630],[571,3705,599],{"className":3706},[625,626],[571,3708],{"className":3709,"style":996},[995],[571,3711,965],{"className":3712},[1000],[571,3714],{"className":3715,"style":996},[995],[571,3717,3719,3722,3725,3728,3731,3734,3737,3740],{"className":3718},[616],[571,3720],{"className":3721,"style":621},[620],[571,3723,1157],{"className":3724},[625],[571,3726,602],{"className":3727},[637],[571,3729,596],{"className":3730},[630],[571,3732,599],{"className":3733},[625,626],[571,3735],{"className":3736,"style":996},[995],[571,3738,965],{"className":3739},[1000],[571,3741],{"className":3742,"style":996},[995],[571,3744,3746,3749,3752,3755,3758,3761,3764,3767],{"className":3745},[616],[571,3747],{"className":3748,"style":621},[620],[571,3750,1135],{"className":3751},[625],[571,3753,602],{"className":3754},[637],[571,3756,596],{"className":3757},[630],[571,3759,599],{"className":3760},[625,626],[571,3762],{"className":3763,"style":996},[995],[571,3765,1138],{"className":3766},[1000],[571,3768],{"className":3769,"style":996},[995],[571,3771,3773,3776,3779],{"className":3772},[616],[571,3774],{"className":3775,"style":621},[620],[571,3777,1127],{"className":3778},[625],[571,3780,602],{"className":3781},[637],[563,3783,3784,3785,4093,4094,4128],{},"Division mit Rest: ",[571,3786,3788,3856],{"className":3787},[574],[571,3789,3791],{"className":3790},[578],[580,3792,3793],{"xmlns":582},[584,3794,3795,3853],{},[587,3796,3797,3799,3801,3807,3809,3811,3817,3819,3821,3823,3825,3827,3829,3831,3833,3835,3837,3839,3845,3847,3849,3851],{},[593,3798,596],{"stretchy":595},[844,3800,1127],{},[1129,3802,3803,3805],{},[590,3804,599],{},[844,3806,1135],{},[593,3808,1138],{},[844,3810,1135],{},[1129,3812,3813,3815],{},[590,3814,599],{},[844,3816,1127],{},[593,3818,965],{},[844,3820,1157],{},[593,3822,602],{"stretchy":595},[593,3824,1738],{},[593,3826,596],{"stretchy":595},[590,3828,599],{},[593,3830,1138],{},[844,3832,1127],{},[593,3834,602],{"stretchy":595},[593,3836,1320],{},[844,3838,1127],{},[1129,3840,3841,3843],{},[590,3842,599],{},[844,3844,1127],{},[593,3846,965],{},[590,3848,599],{},[593,3850,1138],{},[844,3852,1127],{},[604,3854,3855],{"encoding":606},"(2x^3 + 3x^2 - 1) : (x + 2) = 2x^2 - x + 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",[571,4485,4487,4531],{"className":4486},[574],[571,4488,4490],{"className":4489},[578],[580,4491,4492],{"xmlns":582},[584,4493,4494,4528],{},[587,4495,4496,4498,4500,4502,4504,4506,4508,4510,4513,4515,4518,4520,4522,4524,4526],{},[590,4497,563],{},[593,4499,596],{"stretchy":595},[593,4501,965],{},[844,4503,1127],{},[593,4505,602],{"stretchy":595},[593,4507,1320],{},[593,4509,965],{},[844,4511,4512],{},"16",[593,4514,1138],{},[844,4516,4517],{},"12",[593,4519,965],{},[844,4521,1157],{},[593,4523,1320],{},[593,4525,965],{},[844,4527,1341],{},[604,4529,4530],{"encoding":606},"p(-2) = -16 + 12 - 1 = -5",[571,4532,4534,4564,4585,4603,4621],{"className":4533,"ariaHidden":612},[611],[571,4535,4537,4540,4543,4546,4549,4552,4555,4558,4561],{"className":4536},[616],[571,4538],{"className":4539,"style":621},[620],[571,4541,563],{"className":4542},[625,626],[571,4544,596],{"className":4545},[630],[571,4547,965],{"className":4548},[625],[571,4550,1127],{"className":4551},[625],[571,4553,602],{"className":4554},[637],[571,4556],{"className":4557,"style":1376},[995],[571,4559,1320],{"className":4560},[1380],[571,4562],{"className":4563,"style":1376},[995],[571,4565,4567,4570,4573,4576,4579,4582],{"className":4566},[616],[571,4568],{"className":4569,"style":1267},[620],[571,4571,965],{"className":4572},[625],[571,4574,4512],{"className":4575},[625],[571,4577],{"className":4578,"style":996},[995],[571,4580,1138],{"className":4581},[1000],[571,4583],{"className":4584,"style":996},[995],[571,4586,4588,4591,4594,4597,4600],{"className":4587},[616],[571,4589],{"className":4590,"style":1267},[620],[571,4592,4517],{"className":4593},[625],[571,4595],{"className":4596,"style":996},[995],[571,4598,965],{"className":4599},[1000],[571,4601],{"className":4602,"style":996},[995],[571,4604,4606,4609,4612,4615,4618],{"className":4605},[616],[571,4607],{"className":4608,"style":1108},[620],[571,4610,1157],{"className":4611},[625],[571,4613],{"className":4614,"style":1376},[995],[571,4616,1320],{"className":4617},[1380],[571,4619],{"className":4620,"style":1376},[995],[571,4622,4624,4627,4630],{"className":4623},[616],[571,4625],{"className":4626,"style":1267},[620],[571,4628,965],{"className":4629},[625],[571,4631,1341],{"className":4632},[625],". Das ist kein Zufall, bei Division durch ",[571,4635,4637,4662],{"className":4636},[574],[571,4638,4640],{"className":4639},[578],[580,4641,4642],{"xmlns":582},[584,4643,4644,4660],{},[587,4645,4646,4648,4650,4652,4658],{},[593,4647,596],{"stretchy":595},[590,4649,599],{},[593,4651,965],{},[839,4653,4654,4656],{},[590,4655,599],{},[844,4657,846],{},[593,4659,602],{"stretchy":595},[604,4661,976],{"encoding":606},[571,4663,4665,4686],{"className":4664,"ariaHidden":612},[611],[571,4666,4668,4671,4674,4677,4680,4683],{"className":4667},[616],[571,4669],{"className":4670,"style":621},[620],[571,4672,596],{"className":4673},[630],[571,4675,599],{"className":4676},[625,626],[571,4678],{"className":4679,"style":996},[995],[571,4681,965],{"className":4682},[1000],[571,4684],{"className":4685,"style":996},[995],[571,4687,4689,4692,4732],{"className":4688},[616],[571,4690],{"className":4691,"style":621},[620],[571,4693,4695,4698],{"className":4694},[625],[571,4696,599],{"className":4697},[625,626],[571,4699,4701],{"className":4700},[869],[571,4702,4704,4724],{"className":4703},[873,874],[571,4705,4707,4721],{"className":4706},[878],[571,4708,4710],{"className":4709,"style":883},[882],[571,4711,4712,4715],{"style":886},[571,4713],{"className":4714,"style":891},[890],[571,4716,4718],{"className":4717},[895,896,897,898],[571,4719,846],{"className":4720},[625,898],[571,4722,906],{"className":4723},[905],[571,4725,4727],{"className":4726},[878],[571,4728,4730],{"className":4729,"style":913},[882],[571,4731],{},[571,4733,602],{"className":4734},[637]," ist der Rest immer ",[571,4737,4739,4763],{"className":4738},[574],[571,4740,4742],{"className":4741},[578],[580,4743,4744],{"xmlns":582},[584,4745,4746,4760],{},[587,4747,4748,4750,4752,4758],{},[590,4749,563],{},[593,4751,596],{"stretchy":595},[839,4753,4754,4756],{},[590,4755,599],{},[844,4757,846],{},[593,4759,602],{"stretchy":595},[604,4761,4762],{"encoding":606},"p(x_0)",[571,4764,4766],{"className":4765,"ariaHidden":612},[611],[571,4767,4769,4772,4775,4778,4818],{"className":4768},[616],[571,4770],{"className":4771,"style":621},[620],[571,4773,563],{"className":4774},[625,626],[571,4776,596],{"className":4777},[630],[571,4779,4781,4784],{"className":4780},[625],[571,4782,599],{"className":4783},[625,626],[571,4785,4787],{"className":4786},[869],[571,4788,4790,4810],{"className":4789},[873,874],[571,4791,4793,4807],{"className":4792},[878],[571,4794,4796],{"className":4795,"style":883},[882],[571,4797,4798,4801],{"style":886},[571,4799],{"className":4800,"style":891},[890],[571,4802,4804],{"className":4803},[895,896,897,898],[571,4805,846],{"className":4806},[625,898],[571,4808,906],{"className":4809},[905],[571,4811,4813],{"className":4812},[878],[571,4814,4816],{"className":4815,"style":913},[882],[571,4817],{},[571,4819,602],{"className":4820},[637],[558,4822,4824],{"id":4823},"typische-fehler","Typische Fehler",[4826,4827,4828,5094,5126],"ul",{},[1065,4829,4830,4831,5053,5054,822],{},"Beim Abziehen nur den ersten Term subtrahieren: ",[571,4832,4834,4890],{"className":4833},[574],[571,4835,4837],{"className":4836},[578],[580,4838,4839],{"xmlns":582},[584,4840,4841,4887],{},[587,4842,4843,4845,4847,4853,4855,4857,4859,4861,4863,4865,4867,4873,4875,4877,4879,4881,4883,4885],{},[593,4844,596],{"stretchy":595},[593,4846,965],{},[1129,4848,4849,4851],{},[590,4850,599],{},[844,4852,1127],{},[593,4854,965],{},[844,4856,1341],{},[590,4858,599],{},[593,4860,602],{"stretchy":595},[593,4862,965],{},[593,4864,596],{"stretchy":595},[593,4866,965],{},[1129,4868,4869,4871],{},[590,4870,599],{},[844,4872,1127],{},[593,4874,1138],{},[590,4876,599],{},[593,4878,602],{"stretchy":595},[593,4880,1320],{},[593,4882,965],{},[844,4884,1348],{},[590,4886,599],{},[604,4888,4889],{"encoding":606},"(-x^2 - 5x) - (-x^2 + x) = -6x",[571,4891,4893,4943,4967,5017,5038],{"className":4892,"ariaHidden":612},[611],[571,4894,4896,4899,4902,4905,4934,4937,4940],{"className":4895},[616],[571,4897],{"className":4898,"style":3113},[620],[571,4900,596],{"className":4901},[630],[571,4903,965],{"className":4904},[625],[571,4906,4908,4911],{"className":4907},[625],[571,4909,599],{"className":4910},[625,626],[571,4912,4914],{"className":4913},[869],[571,4915,4917],{"className":4916},[873],[571,4918,4920],{"className":4919},[878],[571,4921,4923],{"className":4922,"style":1192},[882],[571,4924,4925,4928],{"style":1195},[571,4926],{"className":4927,"style":891},[890],[571,4929,4931],{"className":4930},[895,896,897,898],[571,4932,1127],{"className":4933},[625,898],[571,4935],{"className":4936,"style":996},[995],[571,4938,965],{"className":4939},[1000],[571,4941],{"className":4942,"style":996},[995],[571,4944,4946,4949,4952,4955,4958,4961,4964],{"className":4945},[616],[571,4947],{"className":4948,"style":621},[620],[571,4950,1341],{"className":4951},[625],[571,4953,599],{"className":4954},[625,626],[571,4956,602],{"className":4957},[637],[571,4959],{"className":4960,"style":996},[995],[571,4962,965],{"className":4963},[1000],[571,4965],{"className":4966,"style":996},[995],[571,4968,4970,4973,4976,4979,5008,5011,5014],{"className":4969},[616],[571,4971],{"className":4972,"style":3113},[620],[571,4974,596],{"className":4975},[630],[571,4977,965],{"className":4978},[625],[571,4980,4982,4985],{"className":4981},[625],[571,4983,599],{"className":4984},[625,626],[571,4986,4988],{"className":4987},[869],[571,4989,4991],{"className":4990},[873],[571,4992,4994],{"className":4993},[878],[571,4995,4997],{"className":4996,"style":1192},[882],[571,4998,4999,5002],{"style":1195},[571,5000],{"className":5001,"style":891},[890],[571,5003,5005],{"className":5004},[895,896,897,898],[571,5006,1127],{"className":5007},[625,898],[571,5009],{"className":5010,"style":996},[995],[571,5012,1138],{"className":5013},[1000],[571,5015],{"className":5016,"style":996},[995],[571,5018,5020,5023,5026,5029,5032,5035],{"className":5019},[616],[571,5021],{"className":5022,"style":621},[620],[571,5024,599],{"className":5025},[625,626],[571,5027,602],{"className":5028},[637],[571,5030],{"className":5031,"style":1376},[995],[571,5033,1320],{"className":5034},[1380],[571,5036],{"className":5037,"style":1376},[995],[571,5039,5041,5044,5047,5050],{"className":5040},[616],[571,5042],{"className":5043,"style":1267},[620],[571,5045,965],{"className":5046},[625],[571,5048,1348],{"className":5049},[625],[571,5051,599],{"className":5052},[625,626],", nicht ",[571,5055,5057,5076],{"className":5056},[574],[571,5058,5060],{"className":5059},[578],[580,5061,5062],{"xmlns":582},[584,5063,5064,5073],{},[587,5065,5066,5068,5071],{},[593,5067,965],{},[844,5069,5070],{},"4",[590,5072,599],{},[604,5074,5075],{"encoding":606},"-4x",[571,5077,5079],{"className":5078,"ariaHidden":612},[611],[571,5080,5082,5085,5088,5091],{"className":5081},[616],[571,5083],{"className":5084,"style":1267},[620],[571,5086,965],{"className":5087},[625],[571,5089,5070],{"className":5090},[625],[571,5092,599],{"className":5093},[625,626],[1065,5095,5096,5097,5125],{},"Fehlende Potenzen nicht mit ",[571,5098,5100,5113],{"className":5099},[574],[571,5101,5103],{"className":5102},[578],[580,5104,5105],{"xmlns":582},[584,5106,5107,5111],{},[587,5108,5109],{},[844,5110,846],{},[604,5112,846],{"encoding":606},[571,5114,5116],{"className":5115,"ariaHidden":612},[611],[571,5117,5119,5122],{"className":5118},[616],[571,5120],{"className":5121,"style":1108},[620],[571,5123,846],{"className":5124},[625]," auffüllen. Dann stehen die Terme in falschen Spalten.",[1065,5127,5128,5129,5190,5191,5219,5220,5289,5290,822],{},"Durch ",[571,5130,5132,5154],{"className":5131},[574],[571,5133,5135],{"className":5134},[578],[580,5136,5137],{"xmlns":582},[584,5138,5139,5151],{},[587,5140,5141,5143,5145,5147,5149],{},[593,5142,596],{"stretchy":595},[590,5144,599],{},[593,5146,1138],{},[844,5148,1127],{},[593,5150,602],{"stretchy":595},[604,5152,5153],{"encoding":606},"(x + 2)",[571,5155,5157,5178],{"className":5156,"ariaHidden":612},[611],[571,5158,5160,5163,5166,5169,5172,5175],{"className":5159},[616],[571,5161],{"className":5162,"style":621},[620],[571,5164,596],{"className":5165},[630],[571,5167,599],{"className":5168},[625,626],[571,5170],{"className":5171,"style":996},[995],[571,5173,1138],{"className":5174},[1000],[571,5176],{"className":5177,"style":996},[995],[571,5179,5181,5184,5187],{"className":5180},[616],[571,5182],{"className":5183,"style":621},[620],[571,5185,1127],{"className":5186},[625],[571,5188,602],{"className":5189},[637]," teilen, wenn die Nullstelle ",[571,5192,5194,5207],{"className":5193},[574],[571,5195,5197],{"className":5196},[578],[580,5198,5199],{"xmlns":582},[584,5200,5201,5205],{},[587,5202,5203],{},[844,5204,1127],{},[604,5206,1127],{"encoding":606},[571,5208,5210],{"className":5209,"ariaHidden":612},[611],[571,5211,5213,5216],{"className":5212},[616],[571,5214],{"className":5215,"style":1108},[620],[571,5217,1127],{"className":5218},[625]," ist. Zur Nullstelle ",[571,5221,5223,5240],{"className":5222},[574],[571,5224,5226],{"className":5225},[578],[580,5227,5228],{"xmlns":582},[584,5229,5230,5238],{},[587,5231,5232],{},[839,5233,5234,5236],{},[590,5235,599],{},[844,5237,846],{},[604,5239,849],{"encoding":606},[571,5241,5243],{"className":5242,"ariaHidden":612},[611],[571,5244,5246,5249],{"className":5245},[616],[571,5247],{"className":5248,"style":859},[620],[571,5250,5252,5255],{"className":5251},[625],[571,5253,599],{"className":5254},[625,626],[571,5256,5258],{"className":5257},[869],[571,5259,5261,5281],{"className":5260},[873,874],[571,5262,5264,5278],{"className":5263},[878],[571,5265,5267],{"className":5266,"style":883},[882],[571,5268,5269,5272],{"style":886},[571,5270],{"className":5271,"style":891},[890],[571,5273,5275],{"className":5274},[895,896,897,898],[571,5276,846],{"className":5277},[625,898],[571,5279,906],{"className":5280},[905],[571,5282,5284],{"className":5283},[878],[571,5285,5287],{"className":5286,"style":913},[882],[571,5288],{}," gehört der Faktor ",[571,5291,5293,5318],{"className":5292},[574],[571,5294,5296],{"className":5295},[578],[580,5297,5298],{"xmlns":582},[584,5299,5300,5316],{},[587,5301,5302,5304,5306,5308,5314],{},[593,5303,596],{"stretchy":595},[590,5305,599],{},[593,5307,965],{},[839,5309,5310,5312],{},[590,5311,599],{},[844,5313,846],{},[593,5315,602],{"stretchy":595},[604,5317,976],{"encoding":606},[571,5319,5321,5342],{"className":5320,"ariaHidden":612},[611],[571,5322,5324,5327,5330,5333,5336,5339],{"className":5323},[616],[571,5325],{"className":5326,"style":621},[620],[571,5328,596],{"className":5329},[630],[571,5331,599],{"className":5332},[625,626],[571,5334],{"className":5335,"style":996},[995],[571,5337,965],{"className":5338},[1000],[571,5340],{"className":5341,"style":996},[995],[571,5343,5345,5348,5388],{"className":5344},[616],[571,5346],{"className":5347,"style":621},[620],[571,5349,5351,5354],{"className":5350},[625],[571,5352,599],{"className":5353},[625,626],[571,5355,5357],{"className":5356},[869],[571,5358,5360,5380],{"className":5359},[873,874],[571,5361,5363,5377],{"className":5362},[878],[571,5364,5366],{"className":5365,"style":883},[882],[571,5367,5368,5371],{"style":886},[571,5369],{"className":5370,"style":891},[890],[571,5372,5374],{"className":5373},[895,896,897,898],[571,5375,846],{"className":5376},[625,898],[571,5378,906],{"className":5379},[905],[571,5381,5383],{"className":5382},[878],[571,5384,5386],{"className":5385,"style":913},[882],[571,5387],{},[571,5389,602],{"className":5390},[637],{"title":5392,"searchDepth":5393,"depth":5393,"links":5394},"",2,[5395,5396,5397],{"id":560,"depth":5393,"text":561},{"id":1294,"depth":5393,"text":1295},{"id":4823,"depth":5393,"text":4824},[5399,5402,5404,5407,5410,5413,5416,5419,5422,5425],{"lhs":5400,"rhs":5401},"(x^2 - x - 6)*(x - 1)","x^3 - 2*x^2 - 5*x + 6",{"lhs":5403,"rhs":846},"1^3 - 2*1^2 - 5*1 + 6",{"lhs":5405,"rhs":5406},"x^2*(x - 1)","x^3 - x^2",{"lhs":5408,"rhs":5409},"(x^3 - 2*x^2 - 5*x) - (x^3 - x^2)","-x^2 - 5*x",{"lhs":5411,"rhs":5412},"-x*(x - 1)","-x^2 + x",{"lhs":5414,"rhs":5415},"(-x^2 - 5*x + 6) - (-x^2 + x)","-6*x + 6",{"lhs":5417,"rhs":5418},"x^2 - x - 6","(x - 3)*(x + 2)",{"lhs":5420,"rhs":5421},"(-x^2 - 5*x) - (-x^2 + x)","-6*x",{"lhs":5423,"rhs":5424},"(2*x^2 - x + 2)*(x + 2) - 5","2*x^3 + 3*x^2 - 1",{"lhs":5426,"rhs":4112},"2*(-2)^3 + 3*(-2)^2 - 1","d \\neq 0,\\ \\operatorname{grad} r \u003C \\operatorname{grad} d","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d \\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 mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace 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d\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=\"mop\">\u003Cspan class=\"mord mathrm\">grad\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">grad\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan 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