Beginning Algebra, 11th Edition

Divide each term by.

Quotient rule

=- 3 x^3 +

7 x^2

4

+ 1

=- 3 x^3 -

7 x^2

- 4

- 1 - 12

= - 4 x

12 x^4

- 4 x

-

7 x^3

- 4 x

-

4 x

- 4 x

12 x^4 - 7 x^3 - 4 x

- 4 x

Write in

descending

powers.

Be sure to include

1 in the answer.

Checkby multiplying. NOW TRY

Dividing a Polynomial by a Monomial

Divide by

NOW TRY

OBJECTIVE 2 Divide a polynomial by a polynomial. As shown in the box,

we use a method of “long division” to divide a polynomial by a polynomial (other than

a monomial). Both polynomials must first be written in descending powers..

= 6 x^3 y^8 - 5 x^2 y^6 + 4 xy^4 - 3 y^2 +

10

3 xy

=

180 x^4 y^10

30 xy^2

-

150 x^3 y^8

30 xy^2

+

120 x^2 y^6

30 xy^2

-

90 xy^4

30 xy^2

+

100 y

30 xy^2

180 x^4 y^10 - 150 x^3 y^8 + 120 x^2 y^6 - 90 xy^4 + 100 y

30 xy^2

180 x^4 y^10 - 150 x^3 y^8 + 120 x^2 y^6 - 90 xy^4 + 100 y 30 xy^2.

EXAMPLE 4

Dividing Whole Numbers Dividing Polynomials

Step 1

Divide 6696 by 27. Divide by

Step 2

66 divided by divided by

2

54 8 x^3 + 12 x^2

27  6696 2 x+ 3  8 x^3 - 4 x^2 - 14 x+ 15

4 x^2

2 # 27 = 54 4 x^212 x+ 32 = 8 x^3 + 12 x^2

27 = 2. 8 x^32 x= 4 x^2.

27  6696 2 x+ 3  8 x^3 - 4 x^2 - 14 x+ 15

8 x^3 - 4 x^2 - 14 x+ 15 2 x+ 3.

NOW TRY
EXERCISE 3
Divide
by - 5 y^2.

7 y^4 - 40 y^5 + 100 y^2

NOW TRY ANSWERS

3. 8 y^3 -

7 y^2

5

• 20

NOW TRY
EXERCISE 4
Divide
12 mn by 7m^2 n.

35 m^5 n^4 - 49 m^2 n^3 +

4. 5 m^3 n^3 - 7 n^2 +
   12
   7 m

342 CHAPTER 5 Exponents and Polynomials

(continued)

Dividing a Polynomial by a Monomial with a

Negative Coefficient

Divide by

Write the polynomial in descending powers as before

dividing.

12 x^4 - 7 x^3 - 4 x

- 7 x^3 + 12 x^4 - 4 x - 4 x.

EXAMPLE 3

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