Question

几道分解因式的题目

x^3-9x^2+27x-27
a^4+4
x^3+2x^2-5x-6
请写详细过程，谢谢

Answer 1

解：(1)x^3-9x^2+27x-27
=x^3-27-(9x^2-27x)
=(x-3)*(x^2+3x+9)-9x(x-3)
=(x-3)(x^2+3x+9-9x)
=(x-3)(x^2-6x+9)
=(x-3)(x-3)^2
=(x-3)^3
(2)a^4+4
=(a^4+2a^3+2a^2)-(2a^3+4a^2+4a)+(2a^2+4a+4)
=a^2(a^2+2a+2)-2a(a^2+2a+2)+2(a^2+2a+2)
=(a^2+2a+2)(a^2-2a+2)
(3)x³+2x²-5x-6
=(x³+x²)+(x²-5x-6)
=x²(x+1)+(x-6)(x+1)
=(x²+x-6)(x+1)
=(x-2)(x+3)(x+1)