因数 w^2+w^{12}+w^{32}+w^{42}

解

因数

w^{2} + w^{12} + w^{32} + w^{42}

w^{2} (w^{2} + 1)^{2} (w^{8} - w^{6} + w^{4} - w^{2} + 1)^{2} (w^{20} - w^{10} + 1)

解答ステップ

w^{2} + w^{12} + w^{32} + w^{42}

標準的な形式で書く

= w^{42} + w^{32} + w^{12} + w^{2}

共通項をくくり出す

w^{2} : w^{2} (w^{40} + w^{30} + w^{10} + 1)

= w^{2} (w^{40} + w^{30} + w^{10} + 1)

因数

w^{40} + w^{30} + w^{10} + 1 : (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{20} - w^{10} + 1)

= w^{2} (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{20} - w^{10} + 1)

簡素化

= w^{2} (w^{2} + 1)^{2} (w^{8} - w^{6} + w^{4} - w^{2} + 1)^{2} (w^{20} - w^{10} + 1)