Question

4道因式分解!1.x^3+2x^2-5x-62.x^8+x^7+13.(x^2+5x+6)(x^2+7x+6)-3x^2

Answer 1

1.x^3+2x^2-5x-6 =x^3+x^2+x^2-5x-6
=x^2(x+1)+(x+1)(x-6)
=(x+1)(x^2+x-6)
=(x+1)(x+3)(x-2)
2.x^8+x^7+1
=x^8+x^7+x^6-x^6+1
=x^6(x^2+x+1)-(x^6-1)
=x^6(x^2+x+1)-(x-1)(x^5+x^4+x^3+x^2+x+1)
=x^6(x^2+x+1)-(x-1)((x^5+x^4+x^3)+(x^2+x+1))
=x^6(x^2+x+1)-(x-1)(x^3(x^2+x+1)+(x^2+x+1))
=x^6(x^2+x+1)-(x-1)(x^3+1)(x^2+x+1)
=(x^2+x+1)(x^6-x^4+x^3+x-1)
3.(x^2+5x+6)(x^2+7x+6)-3x^2
=[(x^2+6)+5x]*[(x^2+6)+7x]-3x^2
=(x^2+6)^2+12x(x^2+6)+35x^2-3x^2
=(x^2+6)^2+12x(x^2+6)+32x^2
=(x^2+6+4x)(x^2+6+8x)
4.(x^2+3x+2)(4x^2+8x+3)-90
=（x+2）（x+1）（2x+1）（2x+3）-90
=（x+2）（2x+1）（x+1）（2x+3）-90
=（2x^2+5x+2）(2x^2+5x+3)-90
=(2x^2+5x)^2+5(2x^2+5x)+6-90
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x-7)(2x^2+5x+12)
=(2x+7)(x-1)(2x^2+5x+12)