请大家帮帮忙,我有一道数学题不会做,这是一道因式分解的题,而且要用十字相乘法做!题目是:(x2-7x+6)(x2-x-6)+56请大家写出解题思路,谢谢!(x的二次方减7x加6)乘以(x的二次方减x减6)加56

问题描述:

请大家帮帮忙,我有一道数学题不会做,这是一道因式分解的题,而且要用十字相乘法做!
题目是:(x2-7x+6)(x2-x-6)+56
请大家写出解题思路,谢谢!
(x的二次方减7x加6)乘以(x的二次方减x减6)加56

(x2-7x+6)(x2-x-6)+56
=(x-6)(x-1)(x-3)(x+2)+56
=[(x-6)(x+2)][(x-3)(x-1)]+56
=(x^2-4x-12)(x^2-4x+3)+56
设x^2-4x-12=A。
原式=A*(A+15)+56
=(A+7)(A+8)
=(x^2-4x-5)(x^2-4x-4)
=(x+1)(x-5)(x-2-2根号2)(x-2+2根号2)

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

.(x的平方-7x+6)(x的平方-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=(x-1)(x-3)(x-6)(x+2)+56
=(x2-4x+3)(x2-4x-12)+56
设x2-4x+3=A.得
A*(A-15)+56
=A2-15A+56
=(A-7)(A-8)
=(x2-4x-4)(x2-4x-5)
=(x2-4x-4)(X-5)(X+1)