Name:_____________________________
Dividing Polynomials
Date:_____ Period:____
Dividing Polynomials:
When we want to divide a polynomial by a monomial, we can simply divide each part
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 that 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 problems above, there was no remainder. What happens if there is a
remainder? If there is a remainder, we can write the remainder as a fraction, just
like we did with “regular” numbers.
Let’s try:
t
2

 3t  9   t  5 
Here’s another example:
2x
3

– 9x 2  15  2x – 5 
Remember, in order to succeed in polynomial division you MUST WRITE NEATLY!!!!
In addition, you can check your work by using multiplication!
Examples:
Show all work. Complete all work on a separate sheet of paper. Make sure to write
neatly!


2. 2x 2  5x  3   x  3


4. b 3  8b 2  20b  b  2
1. x 2  9x  14   x  7 
3. m 2  3m  7  m  2




9. 3w 3  7w 2  4w  3  w  3
11.



6. x 2  10x  24   x  2
7. x 2  12x  45   x  3



5. x 3  y 3   x  y 




8. 4w 3  8w 2  w 2   4w 
10.
6x 2  x  7
3x  1
4x 2  2x  6
2x  3
12. 2h 3  5h 2  22h  2h  3

14.
6x 2  x  7
3x  1
16.
2h 4  h 3  h 2  h  3
h2  1


13. p 3  6   p  1


15. 6y 3  5y 2  2y  1  3y  1 


17. 2x 3  4x  6   x  3



18. b 3  27  b  3