Page 744 - Basic College Mathematics with Early Integers

720 A PPEND I X B I EXPONENTS AND POLYNOMIALS

In general, we have the following.

To Multiply Two Polynomials

Multiply each term of the first polynomial by each term of the second polyno-
mial, and then combine like terms.

Concept Check True or false? When a trinomial is multiplied by a trino-
mial, the result will have at most nine terms. Explain.

A convenient method of multiplying polynomials is to use a vertical format
similar to multiplying real numbers.

2
PRACTICE 9 Example 9 Find the product of 1a - 6a + 32 and 13a + 22 vertically.
2
Multiply 1x + 4x - 12 and
12x + 52 vertically. Solution:
a - 6a + 3
2
* 3a + 2
2a - 12a + 6 Multiply a - 6a + 3 by 2.
2
2
3
2
3a - 18a + 9a Multiply a - 6a + 3 by 3a. Line up like
2
3a - 16a - 3a + 6 terms.
2
3
c
c c c Combine like terms
Notice that this example is the same as Example 8 and of course the products
are the same.
Work Practice 9

Copyright 2012 Pearson Education, Inc.

Answer
3
2
9. 2x + 13x + 18x - 5
Concept Check Answer
True