Question

[Duong Thi Nhuong]

Làm tính chia:

a) \(\left(-2x^4+5x^3-x^2+8\right):\left(3x^2-1\right)\)

b) \(\left(5x^4-2x^2+5\right):\left(3x^2+1\right)\)

Answer 1

[Nguyễn Lê Phước Thịnh]

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

\(=\dfrac{1}{3}\cdot\dfrac{-6x^4+15x^3-3x^2+24}{3x^2-1}\)

\(=\dfrac{1}{3}\cdot\dfrac{-6x^4+2x^2+15x^3-5x-5x^2+\dfrac{5}{3}+5x+\dfrac{67}{3}}{3x^2-1}\)

\(=\dfrac{1}{3}\cdot\left(-2x^2+5x-\dfrac{5}{3}\right)+\dfrac{5x+\dfrac{67}{3}}{3x^2-1}\)

\(=\left(-\dfrac{2}{3}x^2+\dfrac{5}{3}x-\dfrac{5}{9}\right)\cdot\dfrac{5x+\dfrac{67}{3}}{3x^2-1}\)

b: \(\dfrac{5x^4-2x^2+5}{3x^2+1}=\dfrac{5x^4+\dfrac{5}{3}x^2-\dfrac{11}{3}x^2-\dfrac{11}{9}+\dfrac{56}{9}}{3x^2+1}\)

\(=\dfrac{5}{3}x^2-\dfrac{11}{9}+\dfrac{\dfrac{56}{9}}{3x^2+1}\)