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Vocabulary

Review

Chapter 8 242

8-5 Factoring x2 + bx + c

1. Use the Distributive Property. Draw a line from each expression in Column A to an equivalent expression in Column B.

Column A Column B

y(y 1 2) y 3 1 3y 2 2 6y

(2y 2 1)(y 1 2) 2y 2 2

y(y 2 1 3y 2 6) y 2 1 2y

21(y 1 2) 2y(y 1 2) 2 1(y 1 2)

2. Cross out the expressions that are NOT in standard form.

x 2 1 4x 1 3 (y 2 5)(y 1 2) p(p 1 1) r 2 2 1

Vocabulary Builder

trinomial (verb) try noh mee ul

Related Words: polynomial, monomial, binomial

Definition: A trinomial is a polynomial with three terms that are separated by plus or minus signs.

Use Your Vocabulary

3. Error Analysis Jay says that x3 1 5x 2 2 7x 1 2 is a trinomial. Explain why this is not true.

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4. Circle the trinomials.

h3 2 2h 1 4 d3 2 c2 a2 2 b2

r 2 1 3rs 2 24s 2 g 2 1 g 1 1 x 3 1 7x 2y 1 5xy 2 1 y 3

trinomial

HSM11_A1MC_0805_T13402

x2 + 3x – 1

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HSM11_A1MC_0805_T13403

Sum of Factors

1 + = 25

2 + = 14

+ =

+ =

Factors of 24

2,

1, 24

3,

,

Problem 1

Problem 2

243 Lesson 8-5

Factoring x2 1 bx 1 c Where b S 0, c S 0

Got It? What is the factored form of r 2 1 11r 1 24?

5. Complete the factor table. Then circle the pair of factors whose sum is 11.

6. Use the factors you circled in Exercise 5 to complete the factorization below.

r 2 1 11r 1 24 5 (r 1 ) (r 1 )

7. Check your answer using FOIL.

Factoring x2 1 bx 1 c Where b R 0, c S 0

Got It? What is the factored form of y 2 2 6y 1 8?

Underline the correct word(s) to complete each sentence.

8. I need to find factors that multiply / sum to 26 and multiply / sum to 8.

9. At least one of the factors that sum to 26 must be positive / negative .

10. The two factors that multiply to 8 must both be positive / negative .

11. Circle the factors of 8 that sum to 26.

1 and 8 21 and 28 2 and 4 22 and 24

12. Factor the expression.

y 2 2 6y 1 8 5 (y 2 )(y )

13. Check your answer using FOIL.

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Problem 4

Problem 3

Chapter 8 244

Factoring x2 1 bx 1 c Where c R 0

Got It? What is the factored form of n2 1 9n 2 36?

14. Reasoning You are looking for two factors of 236 that sum to 9. Which of the factors has the greater absolute value, the negative factor or the positive factor? How do you know?

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15. Circle the factors of 236 that sum to 9.

(24)(9) (29)(4) (3)(212) (23)(12) (26)(6)

16. Write the factored form of the expression. Check your answer.

Applying Factoring Trinomials

Got It? A rectangle’s area is x 2 2 x 2 72. What are possible dimensions of the rectangle? Use factoring.

17. Circle the number whose factors you want to find.

1 21 2 72 272

18. Circle the sum of the factors.

1 21 2 72 272

19. Reasoning Which of the factors has the greater absolute value, the negative factor or the positive factor? How do you know?

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20. Write pairs of factors of 272. Then circle the pair that sums to 21.

1, 2, 3, 4, 6, 8,

21, 22, , , , ,

21. Write the factored form of the expression.

x 2 2 x 2 72 5 ( )( )

22. Possible dimensions of the rectangle are ( ) and ( ).

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Lesson Check

Math Success

Now Iget it!

Need toreview

0 2 4 6 8 10

245 Lesson 8-5

Factoring a Trinomial With Two Variables

Got It? What is the factored form of m2 1 6mn 2 27n2?

23. Circle the factors of227 that sum to 6.

1 and 227 21 and 27 3 and 29 23 and 9

24. Circle the factored form of m2 1 6mn 2 27n2.

(m 1 n)(m 2 27n) (m 2 n)(m 1 27n) (m 1 3n)(m 2 9n) (m 2 3n)(m 1 9n)

25. Check your answer using FOIL.

• Do you UNDERSTAND?

Tell whether the sum of the factors of the constant term of s 2 1 s 2 30 should be positive or negative when you factor the trinomial.

26. Circle the constant term.

s2 s 30 230

27. Circle the sum of the factors of the constant term.

1 21 2 22 30 230

28. The sum of the factors of the constant term is positive / negative .

Check off the vocabulary words that you understand.

trinomial factor FOIL standard form Distributive Property

Rate how well you can factor trinomials of the form x 2 1 bx 1 c.

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