因数 x^5+x^4+x^3+x^2+x+1

解

因数

x^{5} + x^{4} + x^{3} + x^{2} + x + 1

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

解答ステップ

x^{5} + x^{4} + x^{3} + x^{2} + x + 1

= (x^{5} + x^{4} + x^{3}) + (x^{2} + x + 1)

x^{3}

を

x^{5} + x^{4} + x^{3} : x^{3} (x^{2} + x + 1)

からくくり出す

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

共通項をくくり出す

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

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

因数

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

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