6th Grade Math Textbook, Fundamentals

 &KDSWHU

14-7

Divide Polynomials by Monomials

Objective To model division by a monomial with algebra tiles •To apply the Law of Exponents

to divide a polynomial by a monomial

The triangle at the right has an area of (2x^2  3 x) square units
and a height of 2xunits. What is the length of the base?

To find the length of the base, first transform the formula

for the area of a triangle as b , and substitute the

given dimensions, 2x^2  3 x for Aand 2xfor h:

b

Then to find b, divide the polynomial 4x^2  6 xby the monomial 2x.

When dividing a polynomial by a monomial, make sure the
quotient has the same number of terms as the dividend.
In this case, both the dividend and quotient have 2 terms.

You can use algebra tiles to model

the division of polynomials by monomials.

To model (4x^2  6 x)  2 x, start by building

a rectangle from four x^2 tiles and six xtiles.

Be sure the rectangle has a width of 2x.

To find the quotient, find the length

of the remaining side. In this case, it is 2x 3.

So (4x^2  6 x)  2 x 2 x3.

You can also divide a polynomial by a monomial

algebraically by following these steps:

Rewrite the division of a polynomial by a

monomial as the multiplicationof the polynomial

by the reciprocalof the monomial.

Apply the Distributive Property to distribute the

monomial across the terms of the polynomial.

Simplify if necessary.

Divide the coefficients.

Apply the Law of Exponents for Division to

divide variables.

Simplify.

So the length of the base of the triangle is (2x3) units.

4 x^2  6 x

2 x

2 ( 2 x^2  3 x)

2 x

2 A

h

Remember:abba a•^1 b

(4x^2  6 x) •

 4 x^2 •  6 x•



 () ()

 2 x(21) 3 x(11)

 2 x 3

x

x

6

2

x^2

x

4

2

6 x

2 x

4 x^2

2 x

1

2 x

1

2 x

1

2 x

4 x^2  6 x

2 x

A  2 x^2  3 x

2 x

Remember:

Area of a Triangle

A bh, where Aarea,

bbase, and hheight

1

2

Area of rectangle 4 x^2  6 x

?

xx 111

2 x

x

x