Корни многочлена. Кратные корни
Дан многочлен f(x - с). Расположите этот многочлен по степеням х.
1) пример решения
2(x - 1)5 - (x - 1)4 + 3(x - 1)3 + 4(x - 1)2 - 2(x - 1) + 4; ссылка на лекции
2)
(x - 2)6 + 4(x - 2)5 + 2(x - 2)3 + 2(x - 2)2 - (x - 2) + 1;
3)
(x + 1)5 + 4(x + 1)4 - 3(x + 1)3 + 2(x + 1)2 + 5(x + 1) - 2;
4)
2(x + 2)6 - 3(x + 2)4 + (x + 2)3 - 4(x + 2) - 6;
5)
(x - 3)5 - 2(x - 3)3 + 2(x - 3)2 + (x - 3) - 4;
6)
(x - 1)6 + 2(x - 1)5 + (x - 1)3 - 3(x - 1)2 + 4(x - 1) - 2;
7)
2(x - 3)5 - (x - 3)4 + 3(x - 2)2 + 4(x - 2) + 3;
8)
(x + 3)6 - 2(x + 3)5 - 2(x + 3)3 - (x + 3)2 - 4(x + 3) - 4;
9)
(x + 1)6 - 3(x + 1)4 - 3(x + 1)3 - 2(x + 1)2 - 3(x + 1) + 4;
10)
2(x - 2)5 - 4(x - 2)3 + 2(x - 2)2 - 3(x - 2) + 5;
11)
2(x - 1)6 - 3(x - 1)5 - 2(x - 1)3 + 3(x - 1)2 + 2(x - 1) - 3;
12)
(x + 4)5 - 2(x + 4)4 - 3(x + 4)3 - 2(x + 4)2 - 2(x + 4) - 4;
13)
(x - 4)6 - 3(x - 4)4 - 2(x - 4)3 - 4(x - 4) + 5;
14)
3(x - 3)5 + 2(x - 3)4 - (x - 3)3 - (x - 3)2 + 2(x - 3) + 2;
15)
2(x + 1)6 - (x + 1)4 - 2(x + 1)3 - 3(x + 1)2 - (x + 1) - 5;
16)
(x - 2)6 + 4(x - 2)5 + 2(x - 2)3 + 2(x - 2)2 - (x - 2) + 1;
17)
2(x - 2)6 - (x - 1)5 - 2(x - 1)4 - 3(x - 1)2 - 2(x - 1) - 5;
18)
(x - 3)6 - 4(x - 3)5 - 2(x - 1)3 - 2(x - 1)2 - 3(x - 1) - 4;
19)
2(x + 1)6 - 2(x - 1)4 + 3(x - 1)3 - 2(x - 1)2 - 2(x - 1) + 1;
20)
(x + 2)5 - 4(x + 2)4 + 3(x + 2)3 - 3(x + 2)2 - 4(x + 2) + 2;
Найдите неполное частное и остаток при делении многочлена f(x) на многочлен h(x), если:
1) пример решения
f(x) = x5 - 2x4 - x3 - 6x - 4,
h(x) = x2 - 2x + 3;
2)
f(x) = x6 + 3x5 - 4x4 + 3x2 + 6x - 8,
h(x) = x2 - 4x + 5;
3)
f(x) = x6 - 3x5 + 6x4 + 2x2 - 4x + 6,
h(x) = x2 - 4x + 6;
4)
f(x) = x5 - 3x4 + 2x3 - 2x - 7,
h(x) = x2 - 3x + 4;
5)
f(x) = x5 - 4x4 + 6x3 + 4x + 2,
h(x) = x2 - 2x + 4;
6)
f(x) = x6 - 4x5 + 3x4 - 4x3 + 2x2 + 7x - 4,
h(x) = x2 + 2x + 5;
7)
f(x) = x6 + 3x5 - 4x3 - 2x2 + 8,
h(x) = x2 - 2x + 5;
8)
f(x) = x5 + 7x4 - 6x3 + 8x2 - 6x - 5,
h(x) = x2 + 5x + 7;
9)
f(x) = x5 - 8x4 - 6x3 - 4x2 + 3x + 1,
h(x) = x2 - 5x + 7;
10)
f(x) = x6 + 3x5 - 2x4 + 4x2 - 2x + 3,
h(x) = x2 - x + 4;
11)
f(x) = x6 - 2x5 + 3x3 - 3x2 - 5x - 7,
h(x) = x2 + x + 4;
12)
f(x) = x5 - 2x4 + 6x3 + 5x2 - 6x - 2,
h(x) = x2 - x + 3;
13)
f(x) = x6 - 2x5 + 4x3 - 2x2 + 3x - 5,
h(x) = x2 + x + 3;
14)
f(x) = x5 + 3x4 - 7x3 + 8x2 - 2x + 4,
h(x) = x2 + 2x + 5;
15)
f(x) = x6 - 4x5 - 2x3 + 4x2 - 3x + 2,
h(x) = x2 - 2x + 5;
16)
f(x) = x7 - 3x5 + 2x4 - 4x3 + 2x - 7,
h(x) = x2 + 2x + 3;
17)
f(x) = x7 - 4x6 - 3x4 - 2x2 + 6x - 1,
h(x) = x2 + 5x + 8;
18)
f(x) = x6 + 2x5 + 7x4 - 6x3 + 2x2 - 4x + 3,
h(x) = x2 - 5x + 8;
19)
f(x) = x6 - 4x5 + 7x4 + 8x3 - 6x2 - 5x + 3,
h(x) = x2 - 4x + 5;
20)
f(x) = x5 - 2x4 + 17x3 + 10x2 - 16x + 9,
h(x) = x2 - 6x + 11;