Answer:
[tex](x+8) + \frac{-4x+31}{x^2+2x+1}[/tex]
Step-by-step explanation:
x^3+10x^2+13x+39/x^2+2x+1
[tex]\frac{x^3+10x^2+13x+39}{x^2+2x+1}[/tex]
We divide it using long division
x +8
-----------------------------------------
[tex]x^2+2x+1[/tex] [tex]x^3+10x^2+13x+39[/tex]
[tex]x^3+2x^2+x[/tex]
------------------------------------------(subtract)
[tex]8x^2+12x+39[/tex]
[tex]8x^2+16x+8[/tex]
-------------------------------------------
[tex]-4x+31[/tex]
Quotient is x+8
Remainder is -4x+3
We write it in the form q(x)+r(x)/ b(x)
[tex](x+8) + \frac{-4x+31}{x^2+2x+1}[/tex]
