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NAME DATE PERIOD

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Chapter 8 105 Glencoe Algebra 1

Study Guide and Intervention

Monomials and Factoring

8-1 Factor Monomials A monomial is in factored form when it is expressed as the product of prime numbers and variables, and no variable has an exponent greater than 1.

Factor each monomial completely.

a. 42a 3 42a
3 = 2 ? 21 a ? a a 42 = 21 ? 2, and a 3 = a ? a ? a = 2 ? 3 ? 7 a a a 21 = 3 ? 7

Thus, 42a

3 in factored form is 2 ? 3 ? 7 a a a. b. -40x 2 y 3 -40x 2 y

3 = -1 ? 40 x

2 y 3

Express -40 as -1 ? 40.

= -1 ? 2 ? 20 ? x ? x ? y ? y ? y 40 = 20 ? 2, x 2 = x ? x, and y 3 = y ? y ? y

1 ? 2 ? 2 ? 10 ? x ? x ? y ? y ? y 20 = 10 ? 2

= -1 ? 2 ? 2 ? 2 ? 5 ? x x y y y 10 = 5 ? 2

Thus, -40x

2 y 3 in factored form is -1 ? 2 ? 2 ? 2 ? 5 ? x ? x ? y ? y ? y.

Exercises

Factor each monomial completely.

1. 32x

2

2. 18m

2 n 3. 49a 3 b 2

4. 18y

3

5. -9h

3 jk 2

6. -8d

2

7. 66q

3 r 3

8. 140x

2 y 4 z 9. -ab 2 f 2

10. -17t 11. 625jk

2

12. 47wx

3 yz 2

13. 12r

4

14. -38a

2 b 15. 4mp

Example105_116_ALG1SGIC08_890835.indd 105105_116_ALG1SGIC08_890835.indd 1055/23/08 8:02:18 PM5/23/08 8:02:18 PM

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

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Chapter 8 106 Glencoe Algebra 1

Study Guide and Intervention (continued)

Monomials and Factoring

Greatest Common Factor The product of the common prime factors is called the greatest common factor (GCF) of the numbers. The greatest common factor is the greatest number that is a factor of both original numbers. If two or more integers or monomials have no common prime factors, their GCF is 1 and the integers or monomials are said to be relatively prime.

Find the GCF of 16xy

2 z 2 and 72xyz 3 16xy 2 z 2 = 2 ? 2 ? 2 ? 2 ? x ? y ? y ? z ? z 72xyz
3 = 2 ? 2 ? 2 ? 3 ? 3 ? x ? y ? z ? z ? z

The GCF of 16xy

2 z 2 and 72xyz 3 is 2 ? 2 ? 2 ? x ? y ? z ? z or 8xyz 2

Exercises

Find the GCF of each set of monomials.

1. 49x, 343x

2 2. 4a 7 b, 28ab

3. 96y, 12x, 8y 4. 12a, 18abc

5. 28y

2 , 35xy, 49x 2 yz 6. 2m 2 p, 12mp 2 , 18mp

7. 12x

2 , 32x 2 yz, 60xy 2

8. 18a

3 b 2 , 36a 3 b 2

9. 15mn

2 , 30m 3 n 2 , 90m 3

10. 2x

2 y, 9x 2 y 3 , 18xy 2 11. a 4 b, 8a 3 b 2

12. ab

2 , 5a 4 b 2 , 10b 3

13. 2x

2 y 2 , 8xy 4 , 12x 2 y 14. 6a 2 b 5 , 15a 3 b 4

15. 21a

4 b 7 f 2 , 84a 3 b 4 , 28a 5 b 2 f 3

16. 13x

2 y 5 , 5xy 3 , x 4 y 8-1

Example

105_116_ALG1SGIC08_890835.indd 106105_116_ALG1SGIC08_890835.indd 1065/23/08 8:02:21 PM5/23/08 8:02:21 PM

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