题目内容
将下列多项式分别在下列范围内分解因式：①有理数集Q；②实数集R;③复数集C.
(1)x5y-9xy5;(2)x6+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-
).
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