Question

將下列多項(xiàng)式分別在下列范圍內(nèi)分解因式：①有理數(shù)集Q；②實(shí)數(shù)集R;③復(fù)數(shù)集C.

(1)x⁵y-9xy⁵;(2)x⁶+1.

 

Answer 1

解：(1)①x⁵y-9xy⁵=xy(x⁴-9y⁴)=xy(x²+3y²)(x²-3y²);

②x⁵y-9xy⁵=xy(x²+3y²)(x+y)(x-y);

③x⁵y-9xy⁵=xy(x+yi)(x-yi)(x+y)(x-y).

(2)①x⁶+1=(x²+1)(x⁴-x²+1);

②x⁶+1=(x²+1)(x²+x+1)(x²-x+1);

③x⁶+1=(x+i)(x-i)(x-)(x-)(x-)(x-).