问题 解答题

因式分

(1)(x-y+z)2-(x+y-z)2

(2)x3+6x2+11x+6.

答案

(1)原式=【(x-y+z)+(x+y-z)】【(x-y+z)-(x+y-z)】=2x•(-2y+2z)=-4x(y-z);

(2)原式=x3+6x2+9x+2x+6

=x(x+3)2+2(x+3)

=(x+3)[x(x+3)+2]

=(x+3)(x2+3x+2)

=(x+3)(x+1)(x+2).

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