因式分解 急 10分一道3x^3+7x^2-4x^3+9x^2+26x+24

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因式分解 急 10分一道3x^3+7x^2-4x^3+9x^2+26x+24
因式分解 急 10分一道
3x^3+7x^2-4
x^3+9x^2+26x+24

因式分解 急 10分一道3x^3+7x^2-4x^3+9x^2+26x+24
3x^3+7x^2-4=3x^3+3x^2+4x^2-4=3x^2(x+1)+4(x+1)(x-1)
=(x+1)(3x^2+4x-4)=(x+1)(x+2)(3x-2)
x^3+9x^2+26x+24=(x^3+8x^2+16x)+(x^2+10x+24)
=x(x+4)^2+(x+4)(x+6)=(x+4)(x^2+4x+x+6)
=(x+4)(x+2)(x+3)

3x^3+6x^2+x^2-4=3x(x+1)^2+(x-4)(x+1)=3x(x+2)(3x-2)
x^3+9x^2+26x+24=x(x+4)^2+(x+4)(x+6)=(x+2)(x+3)(x+4)

3x^3+7x^2-4=3x^3+9x^2+6x-2x^2-6x-4=3x(x+1)(x+2)-2(x+1)(x+2)=(3x-2)(x+1)(x+2)
x^3+9x^2+26x+24=x^3+7x^2+12x+2x^2+14x+24=x(x+3)(x+4)+2(x+3)(x+4)=(x+2)(x+3)(x+4)

1.
3x^3+7x^2-4
=(3x^3+3)+(7x^2-7)
=3(x^3+1)+7(x^2-1)
=3(x+1)(x^2+1-x)+7(x+1)(x-1)
=(x+1)(3x^2+4x-4)
2.
x^3+9x^2+26x+24
=(x^3+27)+(9x^2+54x+81)-(28x+84)
=(x+3)(x^2+9+3x)+9(x+3)^2-28(x+3)
=(x+3)(x^2+12x+8)