Question

Cho 2 đa thức: P(x) = \(-5x^3-\dfrac{1}{3}+8x^4+x^2\)

Q(x) = \(x^2-5x-2x^3+x^4-\dfrac{2}{3}\)

Hãy tính P(x) + Q(x) và P(x) - Q(x).

Các bn lm theo cách 1 hàng ngang chứ đừng làm hàng dọc nha !! Mình đg cần gấp

Answer 1

\(P\left(x\right)+Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)+\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)

\(=-5x^3-\dfrac{1}{3}+8x^4+x^2+x^2-5x-2x^3+x^4-\dfrac{2}{3}\)

\(=-5x+\left(x^2+x^2\right)+\left(-5x^3-2x^3\right)+\left(8x^4+x^4\right)+\left(-\dfrac{1}{3}-\dfrac{2}{3}\right)\)

\(=-5x+2x^2-7x^3+9x^4-1\)

\(P\left(x\right)-Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)-\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)

\(=-5x^3-\dfrac{1}{3}+8x^4+x^2-x^2+5x+2x^3-x^4+\dfrac{2}{3}\)

\(=5x+\left(x^2-x^2\right)+\left(-5x^3+2x^3\right)+\left(8x^4-x^4\right)+\left(-\dfrac{1}{3}+\dfrac{2}{3}\right)\)

\(=5x-3x^3+7x^4+\dfrac{1}{3}\)

Answer 2

Ta có: \(P\left(x\right)+Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)+\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)

\(=-5x^3-\dfrac{1}{3}+8x^4+x^2+x^2-5x-2x^3+x^4-\dfrac{2}{3}\)

\(=\left(-5x^3-2x^3\right)-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(8x^4+x^4\right)+\left(x^2+x^2\right)-5x\)

\(=-7x^3+9x^4+2x^2-5x-1\)

Lại có: \(P\left(x\right)-Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)-\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)

\(=-5x^3-\dfrac{1}{3}+8x^4+x^2-x^2+5x+2x^3-x^4+\dfrac{2}{3}\)

\(=\left(-5x^3+2x^3\right)+\left(8x^4-x^4\right)+\left(x^2-x^2\right)+5x-\left(\dfrac{1}{3}-\dfrac{2}{3}\right)\)

\(=-3x^3+7x^4+5x+\dfrac{1}{3}\)

Answer 3

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