Name: __________________________________________________
Dividing Polynomials
Date: ______________
Ms. Cronin
Period: _______
Dividing Polynomials
When we want to divide a polynomial by a monomial, we can simply divide each term of
the polynomial by that monomial. However, we cannot do the same thing when dividing a
polynomial by another polynomial. For this we have to use long division. Long division
involving polynomials is similar to the long division you learned in elementary school.
Let’s try an example together:
Divide x 2  9x 10 by x 1


Here’s another:
z

2
 2z  24 z  4
In the two previous problems, there was no remainder. What happens if there is a
remainder? In this case we can write the remainder as a fraction over the divisor, just like
we did with “regular” numbers.
Let’s try:
t
2
 3t  9 t  5

In this last example, notice that there is no x term in the dividend. When one of the
polynomials is “missing” a term like this, put a 0 in as a placeholder.
2x
3
 9x 2 15 2x  5

Remember, in order to succeed in polynomial long division you MUST WRITE NEATLY! In
addition, you can check your work using multiplication.
Examples:
Show all work on a separate sheet of paper. Make sure to write neatly!



1.
x
3.
m
5.
x
7.
x
9.
3w
11.
4 x 2  2x  6
2x  3
13.
p
15.
17.






 9x 14  x  7
2
 3m  7 m  2

3
 y 3  x  y 

2
12x  45 x  3

2
3
3
 7w  4w  3 w  3
6y
3
 5y  2y 1 3y 1
2x
3
 4 x  6 x  3
2x
2
4.
b
3
 8b 2  20b b  2
6.
x
2
10x  24 x  2
8.
4w
10.
6x 2  x  7
3x 1
12.
2h
14.
4 x 2  6x  7
2x 1
16.
2h 4  h 3  h 2  h  3
h 2 1
18.
b

2
 6 p 1
2.



2


3
3
3
 5x  3 x  3
 8w 2  w  4w
 5h 2  22h 2h  3
 27 b  3