Pre-Algebra Demystified

Division of a Polynomial by a Monomial

To divide a polynomial by a monomial, divide each term in the polynomial by
the monomial.

EXAMPLE
Divide 15x^2 þ10x by 5x.

SOLUTION

15x^2 þ10x

5x

¼

15x^2

5x

þ

10x

5x

¼3xþ 2

EXAMPLE

Divide 6x^2 y^3 þ12x^4 y^2 (
3xy)

SOLUTION

6x^2 y^3 þ12x^4 y^2


3xy

¼

6x^2 y^3


3xy

þ

12x^4 y^2


3xy

¼
2xy^2 
4x^3 y

EXAMPLE

Divide 15x^3
10x^2 þ5x by 5.

SOLUTION

15x^3 
10x^2 þ5x

5

¼

15x^3

5

þ

10x^2

5

þ

5x

5

¼3x^3 
2x^2 þx

PRACTICE

Divide:

1. (21x^2
   14x)7x


2. (30x^2 þ20xþ15) 5


3. (18x^2 y^3 þ12x^4 y^2 )(
   6x)


4. (a^3 b^2 þ2a^4 b
   5a^2 b^2 )ab


5. (8x^3 y^2 z
   12x^4 yz^2 )(
   4xyz)

ANSWERS

1. 3x
   2


2. 6x^2 þ4xþ 3


3. 
   3xy^3
   2x^3 y^2


4. a^2 bþ2a^3
   5ab


5. 
   2x^2 yþ3x^3 z

CHAPTER 12 Monomials and Polynomials 247