Beginning Algebra, 11th Edition

Graphing Simple Polynomials
To graph a simple polynomial equation such as
plot points near the vertex. (In this chapter,
all parabolas have a vertex on the x-axis or the y-axis.)

y=x^2 - 2,

Graph y=x^2 - 2.

CONCEPTS EXAMPLES

xy

2

0

1

22

• 1


• 2


• 1 - 1


• 2

x

y

(^02)
–2
y = x^2 – 2

5.5 Multiplying Polynomials

General Method for Multiplying Polynomials
Multiply each term of the first polynomial by each term
of the second polynomial. Then add like terms.

Multiply.

12 x^4 - 7 x^3 - 4 x^2 - 22 x- 21

12 x^4 - 16 x^3 + 8 x^2 - 28 x

9 x^3 - 12 x^2 + 6 x- 21

4 x+ 3

3 x^3 - 4 x^2 + 2 x- 7

5.6 Special Products

Square of a Binomial

Product of the Sum and Difference of Two Terms

1 xy 21 xy 2 x^2 y^2

1 xy 22 x^2  2 xyy^2

1 xy 22 x^2  2 xyy^2

Multiply.

14 a+ 3214 a- 32 = 16 a^2 - 9

12 m- 5 n 22 = 4 m^2 - 20 mn+ 25 n^2

13 x+ 122 = 9 x^2 + 6 x+ 1

5.7 Dividing Polynomials

Dividing a Polynomial by a Monomial
Divide each term of the polynomial by the monomial.

Dividing a Polynomial by a Polynomial
Use “long division.”

ab

c



a

c



b

c

Divide.

4 x^3 - 2 x^2 + 6 x- 9

2 x

= 2 x^2 - x+ 3 -

9

2 x

FOIL Method for Multiplying Binomials

Step 1 Multiply the two First terms to get the first term
of the product.

Step 2 Find the Outer product and the Inner product,
and mentally add them, when possible, to get
the middle term of the product.

Step 3 Multiply the two Last terms to get the last term
of the product.

Add the terms found in Steps 1–3.

Multiply.

F

O, I

L

The product is 10 x^2 + 7 x- 12.

31 - 42 =- 12

2 x 1 - 42 + 315 x 2 = 7 x

2 x 15 x 2 = 10 x^2

12 x+ 3215 x- 42

Divide each term

in the numerator

by 2x.

Remainder

The final answer is 2x- 5 + 3 x-+^14.

- 1

• 15 x- 20


• 15 x- 21

6 x^2 + 8 x

3 x+ 4  6 x^2 - 7 x- 21

2 x- 5

CHAPTER 5 Summary 351