因式分解:x^4+8x^3+15x^2-4x-20(过程)
问题描述：
因式分解:x^4+8x^3+15x^2-4x-20(过程)
答
x^4+8x^3+15x^2-4x-20=x^2(x^+8x+15)-4(x+5)=x^2(x+3)(x+5)-4(x+5)=(x-5)[x^2(x-3)-4]=(x-5)(x^3-3x^2-4)
x----- +3
x----- +5
x^2+8x+15
答
x^4+8x^3+15x^2-4x-20
=x^2(x^2+8x+15)-4(x+5)
=x^2(x+5)(x+3)-4(x+5)
=(x+5)[(x+3)x^2-4]
=(x+5)(x^3+3x^2-4)
=(x+5)(x^3+2x^2+x^2-4)
=(x+5)[x^2(x+2)+(x+2)(x-2)]
=(x+5)(x+2)(x^2+x-2)
=(x+5)(x+2)(x-1)(x+2)
=(x+5)(x-1)[(x+2)^2]