Question

Select the correct answer. Rewrite the expression x^3+10x^2+13x+39/x^2+2x+1 in the form q(x)+r(x)/b(x).

Answer 1

1 step: Divide the polynomial $x^3+10x^2+13x+39$ by the polynomial $x^2+2x+1$ with remainder:

$x^3+10x^2+13x+39=(x^2+2x+1)(x+8)+(-4x+31).$

Here $x+8$ is quotient and $-4x+31$ is remainder.

2 step: Substitute previous result into the fraction:

$\dfrac{x^3+10x^2+13x+39}{x^2+2x+1}=\dfrac{(x^2+2x+1)(x+8)+(-4x+31)}{x^2+2x+1}=\\ \\=\dfrac{(x^2+2x+1)(x+8)}{x^2+2x+1}+\dfrac{-4x+31}{x^2+2x+1}=(x+8)+\dfrac{-4x+31}{x^2+2x+1}.$

Answer: correct choice is A.