1. Dividing Polynomials

2. 3x3 4x2 x 2 1 1 1 1 Dividing by a Monomial
If the divisor only has one term, split the polynomial up into a fraction for each term.
divisor
Now reduce each fraction.
3x3
4x2 x 2 1 1 1 1

3. Divide without using a calculator.

4. Subtract (which changes the sign of each term in the polynomial)
Long Division
If the divisor has more than one term, perform long division. You do the same steps with polynomial division as with integers. Let's do two problems, one with integers you know how to do and one with polynomials and copy the steps.
Subtract (which changes the sign of each term in the polynomial)
Now multiply by the divisor and put the answer below. x
+ 11 2 1
Bring down the next number or term
Multiply and put below
Now divide 3 into or x into 11x
First divide 3 into or x into x2
x x2 + 8x - 5
Remainder added here over divisor 64
x2 – 3x
subtract 5 8
11x
- 5 32
11x - 33
This is the remainder 26 28
So we found the answer to the problem x2 + 8x – 5  x – 3 or the problem written another way:

5. Remainder added here over divisor
Let's Try Another One
If any powers of terms are missing you should write them in with zeros in front to keep all of your columns straight.
Subtract (which changes the sign of each term in the polynomial) y
- 2
Write out with long division including 0y for missing term
Multiply and put below
Bring down the next term
Multiply and put below
y y2 + 0y + 8
Divide y into y2
Divide y into -2y
Remainder added here over divisor
y2 + 2y
subtract
-2y
+ 8
- 2y - 4
This is the remainder 12