因数 x^{n+2}+x^3+x^n+x+x^2+1

解

因数

x^{n + 2} + x^{3} + x^{n} + x + x^{2} + 1

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

解答ステップ

x^{n + 2} + x^{3} + x^{n} + x + x^{2} + 1

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

= x^{2} x^{n} + x^{3} + x^{n} + x + x^{2} + 1

共通項をくくり出す

x^{n}

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

書き換え

= (x^{2} + 1) x^{n} + x^{3} + x + 1 \cdot (x^{2} + 1)

共通項をくくり出す

(x^{2} + 1)

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

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

x^{3} = x x^{2}

= (x^{2} + 1) (x^{n} + 1) + x x^{2} + x

共通項をくくり出す

x

= (x^{2} + 1) (x^{n} + 1) + x (x^{2} + 1)

共通項をくくり出す

(x^{2} + 1)

= (x^{2} + 1) (x^{n} + 1 + x)