因数 6(x^2-4x+4)^2+(x^2-4x+4)-1

解

因数

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

(3 x^{2} - 12 x + 11) (2 x^{2} - 8 x + 9)

解答ステップ

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

式をグループに分ける

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

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

を

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

からくくり出す

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

共通項をくくり出す

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

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

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

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

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

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

拡張

3 (x - 2)^{2} - 1 : 3 x^{2} - 12 x + 11

= (3 x^{2} - 12 x + 11) (2 (x - 2)^{2} + 1)

拡張

2 (x - 2)^{2} + 1 : 2 x^{2} - 8 x + 9

= (3 x^{2} - 12 x + 11) (2 x^{2} - 8 x + 9)