Long division of a polynomial - please help!

Question

I'm really having trouble understanding how to solve this problem:

 

"Use long division to express f(x) in the form f(x) = Q(x) + [R(x) ÷ (x² -1)], where Q(x) is the quotient and R(x) is the remainder, when dividing 2x³ + 2x by x² - 1."

I set it up like:

 

x² + 0x + 1 √2x³ + 0x² + 2x + 0

I divide x² by 2x³ and I get 2x, which I put on the top. Then I distribute and I ultimately end up with "2x" in the quotient and "4x+0" in the remainder. However, I don't know what to do from there. 

Answer 1

The long division process will give you a quotient of 2x and a remainder of 4x.

 

The setup that you presented is incorrect.

 

Q(x) = 2x, R(x) = 4x.

 

Present your answer exactly as you are directed to do.