Question

Select the correct answer.
Rewrite the expression in the form

Answer 1

The answer is A.

Explanation:

just took the test and got it right

Answer 2

Explanation:

Alright, lets get started.

If the rational expression is converted into
`q(x)+(r(x))/(b(x))`, then it must be equal to
`(q(x)*b(x)+r(x))/(b(x))`

So, checking for first option :

`(x+8)+(-4x+31)/(x^2+2x+1)`

`((x+8)*(x^2+2x+1)+(-4x+31))/(x^2+2x+1)`

Foiling

`(x^3+2x^2+x+8x^2+16x+8-4x+31)/(x^2+2x+1)`

`(x^3+10x^2+13x+39)/(x^2+2x+1)` which is equivalent to given expression.

It means option 1 is correct answer :

`(x+8)+(-4x+31)/(x^2+2x+1)` : Answer

Hope it will help :)