因数 (x-1)^4+5(x-1)^2+9

解

因数

(x - 1)^{4} + 5 (x - 1)^{2} + 9

x^{4} - 4 x^{3} + 11 x^{2} - 14 x + 15

解答ステップ

(x - 1)^{4} + 5 (x - 1)^{2} + 9

(x - 1)^{4} : x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

= x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 + 5 (x - 1)^{2} + 9

(x - 1)^{2} : x^{2} - 2 x + 1

= x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 + 5 (x^{2} - 2 x + 1) + 9

拡張

5 (x^{2} - 2 x + 1) : 5 x^{2} - 10 x + 5

= x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 + 5 x^{2} - 10 x + 5 + 9

簡素化

x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 + 5 x^{2} - 10 x + 5 + 9 : x^{4} - 4 x^{3} + 11 x^{2} - 14 x + 15

= x^{4} - 4 x^{3} + 11 x^{2} - 14 x + 15