因数 x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4

解

因数

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

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

解答ステップ

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

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

x

を

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

からくくり出す

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

共通項をくくり出す

(x^{4} + x^{2} y^{2} + y^{4}) : (x^{4} + x^{2} y^{2} + y^{4}) (x + 1)

= (x^{4} + x^{2} y^{2} + y^{4}) (x + 1)

因数

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

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