题目

分解因式：（1）-x^n+2+3x^n+1+2x^n-6x^n-1 (2)(x^2+3x+1)(x^2+3x-3)-5 (3)(x^2-7x+6)(x^2-x-6)+56

提问时间：2021-02-16

答案

（1）-x^(n+2)+3x^(n+1)+2x^n-6x^(n-1)
=-x^(n-1)(x^3-3x^2-2x+6)
=-x^(n-1)[(x^3-3x^2)-(2x-6)]
=-x^(n-1)[x^2(x-3)-2(x-3)]
=-x^(n-1)(x-3)(x^2-2)

(2)(x^2+3x+1)(x^2+3x-3)-5
=(x^2+3x)^2-2(x^2+3x)-3-5
=(x^2+3x)^2-2(x^2+3x)-8
=(x^2+3x-4)(x^2+3x+2)
=(x+4)(x-1)(x+1)(x+2)

(3)(x^2-7x+6)(x^2-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=[(x-1)(x-3)][(x-6)(x+2])+56
=(x^2-4x+3)(x^2-4x-12)+56
=(x^2-4x)^2-9(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x^2-4x-4)(x-5)(x+1)