Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Vocabulary

Review

Chapter 8 254

8-8 Factoring by Grouping

1. Draw a line from each expression in Column A to the GCF of the terms of the expression in Column B.

Column A Column B

4x2 1 6x 3x

7x3 2 14x2 3

3x2 2 12x 2x 1 1

18x2 2 33x 1 12 7x2

5(2x 1 1) 1 2(2x 1 1) 2x

2. Explain why 4 is NOT the GCF of 12 and 24.

_______________________________________________________________________

_______________________________________________________________________

Vocabulary Builder

cube (noun) kyoob

Related Words: cubic, perfect cube

Definition: For any number a, the cube of a is equal to a 3 a 3 a. A cube is a third power, such as 63 or (2y 2 4)3.

Examples: 53, 2x 3, (a 1 b)3

Use Your Vocabulary

3. Circle each number that is the cube of an integer.

3 8 12 27 30

4. Cross out the expressions that are NOT cubic polynomials.

3x2 4x3 1 1 2x2 1 5x 2 7 6x3 2 x2 1 3x

HSM12A1MC_0808.indd 254 3/9/11 3:31:24 PM

Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.Problem 1

Problem 2

Write the three factors of the polynomial.

Factor.

2h3 + 3h2 = h2(

3 ∙ , 2h + , and h2 +

+

Factor.

4h + 6 = 2( +

Factor out the GCF.

6h4 + 9h3 + 12h2 + 18h

The GCF of the terms is .

( 6) + + +

Group the terms with the greatest degrees.

+

Group the other terms.

+

HSM11_A1MC_0808_T13407

Write the factored polynomial.

6h4 + 9h3 + 12h2 + 18h =

) )

255 Lesson 8-8

Factoring a Cubic Polynomial

Got It? What is the factored form of 8t 3 1 14t 2 1 20t 1 35?

5. Rewrite the polynomial by grouping the two terms with the highest degrees and grouping the other terms.

1

6. Factor the GCF from each pair of terms.

(4t 1 7) 1 ( 1 7)

7. Now factor 8t 3 1 14t 2 1 20t 1 35.

( 1 )( 1 )

8. Check your answer using FOIL.

Factoring a Polynomial Completely

Got It? What is the factored form of 6h4 1 9h3 1 12h2 1 18h? Factor completely.

9. Complete the flow chart.

HSM12A1MC_0808.indd 255 3/9/11 3:31:19 PM

Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Problem 3

art FPO

Summary Factoring Polynomials

Chapter 8 256

Finding the Dimensions of a Rectangular Prism

Got It? Geometry A rectangular prism has volume 60x 3 1 34x 2 1 4x. What expressions can represent the dimensions of the prism? Use factoring.

10. Circle the GCF of the terms of the polynomial.

x 2x x2

11. Circle the expression with the GCF factored out.

x(60x2 1 34x 1 4) 2x(30x2 1 17x 1 2) x2(60x 1 34 1 4)

12. The expression ac for the trinomial factor in Exercise 11 is .

13. In order to rewrite bx so you can factor the trinomial, you must find the two numbers

whose product is and whose sum is .

14. Rewrite bx in the polynomial below.

30x 2 1 12x 1 x 1 2

15. Factor the polynomial by grouping.

16. The expressions , , and can represent the dimensions of the prism.

17. Reasoning Can the expressions x, 12x 1 2, and 5x 1 2 represent the dimensions of the prism? Explain.

_______________________________________________________________________

_______________________________________________________________________

Vocabulary Complete each sentence with a word from the list below.

binomial factors common factors factor group

18. 9 out the greatest common factor (GCF).

19. If a polynomial has two or three terms, look for a difference of two squares, a perfect-square trinomial, or a pair of 9.

20. If the polynomial has four or more terms, 9 terms to find common binomial factors.

21. As a final check, make sure there are no 9 other than 1.

HSM12A1MC_0808.indd 256 3/9/11 3:31:15 PM

Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Now Iget it!

Need toreview

0 2 4 6 8 10

Math Success

Lesson Check

Lesson Check

257 Lesson 8-8

Check off the vocabulary words that you understand.

cubic polynomial factoring by grouping

Rate how well you can factor cubic polynomials by grouping.

• Do you UNDERSTAND?

Reasoning Can you factor the polynomial 6q 3 1 2q 2 1 12q 2 3 by grouping? Explain.

24. Group the two terms with the greatest degrees. Group the other two terms.

( 1 ) 1 ( 2 )

25. Factor out the GCF from each pair of terms.

( 1 1) 1 ( 2 1)

26. This time group the first and third terms of the polynomial. Group the other two terms.

( 1 ) 1 ( 2 )

27. Factor out the GCF from each pair of terms.

( 1 2) 1 ( 2 3)

28. Explain why you cannot factor the polynomial by grouping.

_______________________________________________________________________

• Do you know HOW?

Factor the expression 20r 3 1 8r 2 1 15r 1 6.

22. I will use grouping / the perfect-square trinomial rule to factor the expression.

23. Now factor the polynomial.

HSM12A1MC_0808.indd 257 3/9/11 3:31:10 PM