因数 (x+5)^4+2(x+5)^2-1

解

因数

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

x^{4} + 20 x^{3} + 152 x^{2} + 520 x + 674

解答ステップ

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

(x + 5)^{4} : x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625

= x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 (x + 5)^{2} - 1

(x + 5)^{2} : x^{2} + 10 x + 25

= x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 (x^{2} + 10 x + 25) - 1

拡張

2 (x^{2} + 10 x + 25) : 2 x^{2} + 20 x + 50

= x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 x^{2} + 20 x + 50 - 1

簡素化

x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 x^{2} + 20 x + 50 - 1 : x^{4} + 20 x^{3} + 152 x^{2} + 520 x + 674

= x^{4} + 20 x^{3} + 152 x^{2} + 520 x + 674