Respuesta :

kudzordzifrancis

Answer:

D. [tex](x^2+x-1)+\frac{-6}{x+4}[/tex]

Step-by-step explanation:

The given rational expression is

[tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]

We obtain the quotient and remainder using synthetic division.

     1     5    3    -10

-4|       -4   -4    4

      1     1     -1    -6

The quotient is [tex]x^3+x-1[/tex] and the remainder is -6.

The expression becomes;

[tex]\frac{x^3+5x^2+3x-10}{x+4}=(x^2+x-1)+\frac{-6}{x+4}[/tex]

Ashraf82

Answer:

The answer is (D) ⇒ ([tex]x^{2}+x-1)+\frac{-6}{x+4}[/tex]

Step-by-step explanation:

∵ [tex]\frac{x^{3}+5x^{2}+3x-10}{x+4}=x^{2}+\frac{x^{2}+3x-10 }{x+4}[/tex]

∵ [tex]\frac{x^{2}+3x-10 }{x+4}=x+\frac{-x-10}{x+4}[/tex]

∵ [tex]\frac{-x-10}{x+4}=-1+\frac{-6}{x+4}[/tex]

∴ The answer is (x² + x - 1) + (-6)/(x + 4)

Otras preguntas

Q&A Education