1 step: Divide the polynomial [tex]x^3+10x^2+13x+39[/tex] by the polynomial [tex]x^2+2x+1[/tex] with remainder:
[tex]x^3+10x^2+13x+39=(x^2+2x+1)(x+8)+(-4x+31).[/tex]
Here [tex]x+8[/tex] is quotient and [tex]-4x+31[/tex] is remainder.
2 step: Substitute previous result into the fraction:
[tex]\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}.[/tex]
Answer: correct choice is A.
