1. Dividing a Polynomial by a Monomial
Beginning Algebra
Dividing a Polynomial
by a Monomial

2. Dividing Polynomials:
What to Do
How to Do It
9x4  12x3
3x2
1. Divide a binomial by a monomial
using
3x2 1
= (9x4  x3)
the definition of division,
the distributive property
9x4
3x2
12x3  =
the laws of the exponents
= 3x2  4x

3. Dividing Polynomials:
What to Do
How to Do It
2. Divide 6a5  15a7 by - 3a
6a5  15a7
- 3a
using 3a
- 1
the definition of division,
(6a5  15a7)
6a5 3a
15a7 + -
the distributive property
the laws of the exponents.
- 2a4 + 5a6

4. Dividing Polynomials:
What to Do
How to Do It
3. Divide a polynomial by a monomial in the same way, watching signs and powers.
24x5y7  18x4y4 + 3x3y2
- 6x2y2
Divide each term using the distributive property.  +
- 6x2y2
24x5y7
18x4y4
3x3y2
Reduce each fraction to lowest terms:
4x3y5 + 3x2y2  2 x

5. Dividing Polynomials:
What to Do
How to Do It
5x2(6x  3) + 6x3(3x  1) 3x
4. Simplify the numerator
Divide the polynomial by the monomial
18x4 + 24x3  15x2 3x
Divide each term using
the distributive property. +  3x
18x4
24x3
15x2
Reduce each fraction
to lowest terms:
6x x2  5x

6. Dividing Polynomials:
5. Show that  5 by replacing x with 7.
x + 5 x
What to Do
How to Do It
7+ 5 7
 5
x + 5 x
 5
when x = 7 12 7
 5
Note: You cannot cancel a piece of a sum.

7. THE
END