Here are some methods for dividing polynomials. The first is Long Division of polynomials just like you might have used for the problems above.
Here are the steps for long division:
1) Divide the first term of the numerator by the first term of the denominator, and put that answer over the first term of the dividend.
2) Multiply the denominator by that answer, and put that below the numerator.
3) Subtract to that answer and bring the rest of the original dividend down.
4) Repeat these steps, dividing into the new polynomial that was created after the subtraction.
The process continues until the divisor had divided into all of the terms of its degree or or higher. There may be a remainder or the remainder may be zero. The example below shows a long division problem where the remainder is zero.