因式分解a^3-7a^2-4a+28

题目

因式分解a^3-7a^2-4a+28

答案

a^3-7a^2-4a+28
=a^3-2a^2-5a^2-4a+28
=a^2(a-2)-(5a^2+4a-28)
=a^2(a-2)-(a-2)(5a+14)
=(a-2)[a^2-(5a+14)]
=(a-2)(a^2-5a-14)
=(a-2)(a+2)(a-7)