因数 2(x+1)^3-3(x+1)^2-6

解

因数

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

2 x^{3} + 3 x^{2} - 7

解答ステップ

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

(x + 1)^{3} : x^{3} + 3 x^{2} + 3 x + 1

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

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

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

拡張

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

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

拡張

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

= 2 x^{3} + 6 x^{2} + 6 x + 2 - 3 x^{2} - 6 x - 3 - 6

簡素化

2 x^{3} + 6 x^{2} + 6 x + 2 - 3 x^{2} - 6 x - 3 - 6 : 2 x^{3} + 3 x^{2} - 7

= 2 x^{3} + 3 x^{2} - 7