分解因式(x-6)(x-1)(x-3)(x+2)+56
问题描述：
分解因式(x-6)(x-1)(x-3)(x+2)+56
答
(x-6)(x-1)(x-3)(x+2)+56
=x^4 -8x^3+(6+18-12+3-2-6)x^2 +(6x+36x+12x-18x)-36+56
=x^4-8x^3+7x^2 +36x +20
=x^4+x^3 -9x^3-9x^2 +16x^2 +16x+20x +20
=(x+1)(x^3-9x^2+16x+20)
=(x+1)[(x^3-5x^2) -(4x^2-20x)-(4x-20)]
=(x+1)(x-5)(x^2 -4x-4)