分解因式:x(x-1)(x+1)(x+2)-24=______.

问题描述:

分解因式:x(x-1)(x+1)(x+2)-24=______.

原式=x(x+1)(x-1)(x+2)-24 =x(x2-1)(x+2)-24 =x(x3+2x2-x-2)-24 =x4+2x3-x2-2x-24 =(x4-2x3)+4x3-x2-2x-24 =x3(x-2)+4x3-8x2+7x2-2x-24 =(x3+4x2)(x-2)+(7x2-14x)+(12x-24)=(x3+4x2+7x+12...
答案解析:原式去括号变形后,利用十字相乘法分解即可.
考试点:因式分解-十字相乘法等.
知识点:此题考查了因式分解-十字相乘法,熟练掌握十字相乘法是解本题的关键.