因数 (x+3)^2(x+4)+(x-1)x

解

因数

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

x^{3} + 11 x^{2} + 32 x + 36

解答ステップ

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

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

(x + 3)^{2} : x^{2} + 6 x + 9

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

拡張

(x^{2} + 6 x + 9) (x + 4) : x^{3} + 10 x^{2} + 33 x + 36

= x^{3} + 10 x^{2} + 33 x + 36 + (x - 1) x

拡張

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

= x^{3} + 10 x^{2} + 33 x + 36 + x^{2} - x

簡素化

x^{3} + 10 x^{2} + 33 x + 36 + x^{2} - x : x^{3} + 11 x^{2} + 32 x + 36

= x^{3} + 11 x^{2} + 32 x + 36