Phan tich da thuc thanh nhan tu: x^3+3x^2-10x-24 2x^3-11x^2+10x+8 x^4-8x^3+11x^2+8x-12 -3x^4+20x^3-35x^2-10x+48

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1. Đáp án:

   $a) (x -3).(x +2).(x +4)$

   $b) (x -4).(x -2).(2x +1)$

   $c) (x -6).(x -2).(x -1).(x +1)$

   $d) (x -3).(x -2).(x +1).(-3x +8)$

   Giải thích các bước giải:

   $a)$ `x^3 +3x^2 -10x -24 `

   `= x^2.(x -3) +6x.(x -3) +8.(x -3)`

   `= (x -3).(x² +6x +8)`

   `= (x -3).[x.(x +2) +4.(x +2)]`

   `= (x -3).(x +2).(x +4)`

   $b)$ `2x^3 -11x^2 +10x +8`

   `= 2x².(x -4) -3x.(x -4) -2.(x -4)`

   `= (x -4).(2x² -3x -2)`

   `= (x -4).[2x.(x -2) +(x -2)]`

   `= (x -4).(x -2).(2x +1)`

   $c)$ `x^4 -8x^3 +11x^2 +8x -12`

   `= x³.(x -6) -2x².(x -6) -x.(x -6) +2.(x -6)`

   `= (x -6).(x³ -2x² -x +2)`

   `= (x -6).[x².(x -2) -(x -2)]`

   `= (x -6).(x -2).(x² -1)`

   `= (x -6).(x -2).(x -1).(x +1)`

   $d)$ `-3x^4 +20x^3 -35x^2 -10x +48`

   `= -3x³.(x -3) +11x².(x -3) -2x.(x -3) -16.(x -3)`

   `= (x -3).(-3x³ +11x² -2x -16)`

   `= (x -3).[-3x².(x -2) +5x.(x -2) +8.(x -2)]`

   `= (x -3).(x -2).(-3x² +5x +8)`

   `= (x -3).(x -2).[-3x.(x +1) +8.(x +1)]`

   `= (x -3).(x -2).(x +1).(-3x +8)`

    

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2. a)

   `x^3+3x^2-10x-24`

   `⇔x^3+2x^2+x^2+2x-12x-24`

   `⇔x^2(x+2)+x(x+2)-12(x+2)`

   `⇔(x^2+x-12)(x+2)`

   `⇔(x^2-3x+4x-12)(x+2)`

   `⇔[x(x-3)+4(x-3)](x+2)`

   `⇔(x-3)(x+4)(x+2)`

   b)

   `2x^3-11x^2+10x+8`

   `⇔ 2x^3+x^2-12x^2-6x+16x+8`

   `⇔x^2(2x+1)-6x(2x+1)+8(2x+1)`

   `⇔(x^2-6x+8)(2x+1)`

   `⇔(x^2-4x-2x+8)(2x+1)`

   `⇔[x(x-4)-2(x-4)](2x+1)`

   `⇔(x-4)(x-2)(2x+1)`

   c)

   `x^4-8x^3+11x^2+8x-12`

   `⇔x^4-x^3-7x^3+7x^2+3x^2-3x+12x-12`

   `⇔x^3(x-1)-7x^2(x-1)+3x(x-1)+12(x-1)`

   `⇔(x^3-7x^2+3x+12)(x-1)`

   `⇔(x^3+x^2-8x^2-8x+12x+12)(x-1)`

   `⇔[x^2(x+1)-8x(x+1)+12(x+1)](x-1)`

   `⇔(x^2-8x+12)(x+1)(x-1)`

   `⇔(x^2-2x-6x+12)(x-1)(x+1)`

   `⇔[x(x-2)-6(x-2)](x-1)(x+1)`

   `⇔(x-2)(x-6)(x-1)(x+1)`

   d)

   `-3x^4+20x^3-35x^2-10x+48`

   `⇔-(3x^4-20x^3+35x^2+10x-48)`

   `⇔-(3x^4+3x^3-23x^3-23x^2+58x^2+58x-48x-48)`

   `⇔-[3x^3(x+1)-23x^2(x+1)+58x(x+1)-48(x+1)]`

   `⇔-(3x^3-23x^2+58x-48)(x+1)`

   `⇔-(3x^3-6x^2-17x^2+34x+24x-48)(x+1)`

   `⇔-[3x^2(x-2)-17x(x-2)+24(x-2)](x+1)`

   `⇔-(3x^2-17x+24)(x-2)(x+1)`

   `⇔-(3x^2-8x-9x+24)(x-2)(x+1)`

   `⇔-[x(3x-8)-3(3x-8)](x-2)(x+1)`

   `⇔-(x-3)(3x-8)(x-2)(x+1)`

    

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