多项式多于三项的,因式分解时一般需要拆项、添项后分组分解。
如:a^3+3a^2-20a+20
=a^3-2a^2+5a^2-10a-10a+20
=(a^3-2a^2)+(5a^2-10a)-(10a-20)
=a^2(a-2)+5a(a-2)-10(a-2)
=(a-2)(a^2+5a-10).
多项式多于三项的,因式分解时一般需要拆项、添项后分组分解。
如:a^3+3a^2-20a+20
=a^3-2a^2+5a^2-10a-10a+20
=(a^3-2a^2)+(5a^2-10a)-(10a-20)
=a^2(a-2)+5a(a-2)-10(a-2)
=(a-2)(a^2+5a-10).