How do you divide this polynomial using long division?

Question

x^3 - 9 divided by x^2 + 1

If you can show your work, I would really appreciate it. I'm getting stuck even after adding place holders. Thanks in advance.

Answer 1

I'm sure you've seen this several times in class - we just set if up like any other division problem, only in this case we don't have to guess what the multiple to use, just make sure the terms of highest degree cancel. Also, try to make sure that you leave the same amount of space for each term, including the ones whose coefficients are 0 (this greatly reduces confusion) So we have:

.......... x
x² + 1| x³ ..... ...... - 9
.......... x³ ..... + x
......... --------------
.................... .. -x - 9

Now, at this point, the degree of the remainder is already less than the degree of the divisor, so we are done. The answer is x + (-x-9)/(x²+1) or being simplified, x - (x+9)/(x²+1).

Answer 2

Perhaps you're getting stuck because it doesn't divide evenly. The answer is going to be x plus a remainder over (x^2+1)