phân tích đa thành nhân tử a) 2x^4-2x^3-3x^2+X+2 b)-5x^3+2x^2-3x-10 c)x^4-5x^3+3x^2-2x+3 d)x^3-5x^2-2x+24 e)) x^3 -x^2-10x-8

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1. Đáp án:

    

   Giải thích các bước giải:

   a/ $2x^4-2x^3-3x^2+x+2$
   $=2x^4-2x^3-3x^2+3x-2x+2$
   $=(x-1)(2x^3-3x-2)$

   b/ $-5x^3+2x^2-3x-10$
   $=-5x^3-5x^2+7x^2+7x-10x-10$
   $=(x+1)(-5x^2+7x-10)$

   c/ $x^4-5x^3+3x^2-2x+3$
   $=x^4-x^3-4x^3+4x^2-x^2+x-3x+3$
   $=(x-1)(x^3-4x^2-x-3)$

   d/ $x^3-5x^2-2x+24$
   $=x^3+2x^2-7x^2-14x+12x+24$
   $=(x+2)(x^2-7x+12)$
   $=(x+2)(x^2-4x-3x+12)$
   $=(x+2)(x-4)(x-3)$

   e/ $x^3-x^2-10x-8$
   $=x^3+x^2-2x^2-2x-8x-8$
   $=(x+1)(x^2-2x-8)$
   $=(x+1)(x^2+2x-4x-8)$
   $=(x+1)(x+2)(x-4)$
   Chúc bạn học tốt !!

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2. `a) 2x^4-2x^3-3x^2+x+2`

   `=2x^4-2x^3- 3x^2-2x+3x+2`

   `=(2x^4-3x^2-2x)-(2x^3-3x-2)`

   `= x(2x^3-3x-2)-(2x^3-3x-2)`

   `=(2x^3-3x-2)(x-1).`

   `b)-5x^3+2x^2-3x-10`

   `=-5x^3+7x^2 – 5x^2-10x+7x-10`

   `=(-5x^3+7x^2-10x)+(-5x^2+7x-10)`

   `= -x(5x^2−7x+10)-  (5x^2−7x+10)`

   `=(5x^2-7x+10)(-x-1)`

   `=-(5x^2-7x+10)(x+1).`

   `c)x^4-5x^3+3x^2-2x+3`

   `= x^4 – x^3 -4x^3 + 4x^2 – x^2 +x – 3x +3`

   `= (x^4-x^3) – (4x^3-4x^2) – (x^2-x) – (3x-3)`

   `=x^3 (x-1) -4x^2(x-1) – x(x-1) -3(x-1)`

   `=(x-1)(x^3-4x^2-x-3).`

   `d)x^3-5x^2-2x+24`

    `= x^3-4x^2-x^2 + 4x – 6x+24`

   `=  x^2(x-4) – x(x-4)-6(x-4)`

   `=(x-4)(x^2-x-6)`

   `=(x-4)(x^2-3x+2x-6)`

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

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

   `e)x^3 -x^2-10x-8`

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

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

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

   `=(x-4)(x^2+x+2x+2)`

   `=(x-4)[x(x+1)+2(x+1)]`

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

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