Answer:
Step-by-step explanation:
Alright, lets get started.
If the rational expression is converted into [tex]q(x)+\frac{r(x)}{b(x)}[/tex], then it must be equal to [tex]\frac{q(x)*b(x)+r(x)}{b(x)}[/tex]
So, checking for first option :
[tex](x+8)+\frac{-4x+31}{x^2+2x+1}[/tex]
[tex]\frac{(x+8)*(x^2+2x+1)+(-4x+31)}{x^2+2x+1}[/tex]
Foiling
[tex]\frac{x^3+2x^2+x+8x^2+16x+8-4x+31}{x^2+2x+1}[/tex]
[tex]\frac{x^3+10x^2+13x+39}{x^2+2x+1}[/tex] which is equivalent to given expression.
It means option 1 is correct answer :
[tex](x+8)+\frac{-4x+31}{x^2+2x+1}[/tex] : Answer
Hope it will help :)
