分解因式:(x²-7x+6)(x²-x-6)+56

(x²-7x+6)(x²-x-6)+56
=(x-6)(x-1)(x-3)(x+2)+56
=[(x-6)(x+2)][(x-1)(x-3)]+56 （注意此处两两相乘的原则是一次项系数相同）
=(x^2-4x-12)(x^2-4x+3)+56　（把x^2-4x看成一个整体）
=(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) （前一项有实根）
=[(x-(2+2√2)][x+(2+2√2)](x-5)(x+1)

原式
=(x-1)(x-6)(x+2)(x-3)+56
=(x-1)(x-3)(x-6)(x+2)+56
=(x²-4x+3)(x²-4x-12)+56
令x²-4x=t
原式化为
(t+3）（t-12)+56
=t²-9t-36+56
=t²-9t+20
=(t-4)(t-5)
=（x²-4x-4)(x²-4x-5)
=(x²-4x-4)(x-5)(x+1)

(x²-7x+6)(x²-x-6)+56(x-1)(x-6)(x+2)(x-3)+56(x²-4x+3)(x²-4x-12)+56(x²-4x)²-9(x²-4x)-36+56(x²-4x)²-9(x²-4x)+20(x²-4x-4)(x²-4x-5)(x²-4x-4)...

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