Cho các đa thức : f(x) = x^3 – 2x^2 + 3x+1 g(x) = x^3 + x – 1 h(x) = 2x^2 – 1 a, Tìm A

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1. a) `A(x) =2f(x)+ g(x)`

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

   `= 2x^3 – 4x^2 + 6x + 2 + x^3 + x-1`

   `= (2x^3 +x^3) – 4x^2 + (6x +x)  + (2-1)`

   `= 3x^3 – 4x^2 + 7x +1`

   b) `2B(x) + f(x) = h(x)`

   `2B(x) = h(x) – f(x)`

   `2B(x) = (2x^2 -1) – (x^3 – 2x^2 + 3x+1)`

   `2B(x) = 2x^2 -1 – x^3 + 2x^2 – 3x -1`

   `2B(x) = (2x^2 + 2x^2) – (1+1)  – x^3 – 3x`

   `2B(x) = 4x^2 – 2 – x^3 -3x`

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

   `B(x) = 2x^2 – 1 – 1/2 x^3 – 3/2x`

   c) `C(x) = 2g(x) + 3h(x)`

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

   `= 2x^3 + 2x -2 + 6x^2 -3`

   `= 2x^3 + 2x + 6x^2 – (2+3)`

   `=2x^3 + 2x + 6x^2 – 5`

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2. Đáp án + Giải thích các bước giải:

   a)

   `A(x)=2f(x)+g(x)=2(x^3 – 2x^2 + 3x+1)+ x^3 + x – 1`

   `<=>A(x)=2x^3 – 4x^2 + 6x+2+ x^3 + x – 1`

   `<=>A(x)=(2x^3+ x^3) – 4x^2 + (6x+ x)+(2  – 1)`

   `<=>A(x)=3x^3- 4x^2 +7x+1`

   b)

   `2B(x)+f(x)=h(x)`

   `<=>2B(x)=h(x)-f(x)`

   `<=>B(x)=(h(x)-f(x)):2`

   `<=>B(x)=[(2x^2 – 1)-(x^3 – 2x^2 + 3x+1)]:2`

   `<=>B(x)=[2x^2 – 1-x^3+2x^2-3x-1]:2`

   `<=>B(x)=[(2x^2+2x^2) – (1+1)-x^3-3x]:2`

   `<=>B(x)=[4x^2-2-x^3-3x]1/2`

   `<=>B(x)=2x^2-1-1/2 x^3-3/2x`

   c)

   TH1: Đề: `C(x)=2g(x) = 3h(x)`

   `C(x)=2g(x) = 3h(x)`

   `<=>C(x)=3h(x)`

   `<=>C(x)=3(2x^2 – 1)`

   `<=>C(x)=6x^2 -3`

   TH2: Đề: `C(x)=2g(x)+3h(x)`

   `C(x)=2g(x)+3h(x)`

   `<=>C(x)=2(x^3 + x – 1)+3(2x^2 – 1)`

   `<=>C(x)=2x^3 + 2x – 2+6x^2 – 3`

   `<=>C(x)=2x^3 + 2x +6x^2- (2 +3)`

   `<=>C(x)=2x^3 + 2x +6x^2- 5`

    

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