Answer:
[tex]3x^{2} -3x+8-\frac{9}{x+1}[/tex]
Step-by-step explanation:
Since we're dividing the polynomial by [tex](x+1)[/tex], we'll be using -1 to start the division.
Before setting the division up, let's list the coefficients of [tex]x[/tex] from descending powers and the constant.
The coefficient of [tex]x^{3}[/tex] is 3
Since we don't see an [tex]x^{2}[/tex], the coefficient will be 0.
The coefficient of [tex]x[/tex] is 5.
Lastly, the constant, which is the term without the [tex]x[/tex] is -1.
Refer to the attached picture before continuing.
After referring to the picture, we now have the coefficients for the quotient.
The coefficient of [tex]x^{2}[/tex] is 3.
The coefficient of [tex]x[/tex] is -3.
The constant is 8.
Lastly, since the last number is not zero, it's the remainder just like regular division. This can be tricky to remember, but -9 is not the actual remainder.
The remainder is actually [tex]\frac{-9}{x+1}[/tex].
Now putting all the pieces together, we get:
[tex]3x^{2} -3x+8-\frac{9}{x+1}[/tex]
