4-4
PART 2
Factoring Quadratic
Expressions
Vocabulary
Review
1. Circle each perfect square.
4
27
33
64
2. Draw a line from each binomial square to an equivalent perfect square expression.
Column A
Column B
(x 1
x 2 2 4x 1 4
2)2
(x 2 2)2
9x 2 1 6x 1 1
(3x 1 1)2
x 2 1 4x 1 4
Vocabulary Builder
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trinomial (noun) try NOH mee ul
Definition: An expression with three terms is a trinomial.
Examples: x 2 1 4x 1 4, 9x 2 1 6xy 1 y 2 , 2x 2 2 x 2 10, 3x 1 2y 1 7z
Use Your Vocabulary
3. Circle the trinomials.
x2 2 9
4x 2 1 16x 1 16
x 2 1 2xy 1 y 2 1 7
a1b1c
4. Write T for trinomial or B for binomial to describe each expression.
9y 1 5yz 1 16
Problem 3
22x 1 2xy 1 3y 2
16x 2 2 9y 2
2a 1 3b
Factoring ax 2 1 bx 1 c when »a… u 1
Got It? What is the expression 4x 2 1 7x 1 3 in factored form? Check your answers.
5. Complete the diagram at the right.
4x 2 7x 3
r
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12
Lesson 4-4, Part 2
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6. Complete the factor pairs of ac. Then circle the pair that sums to 7.
Q 1,
R
Q 2,
R
Q 3,
R
7. Use your answer to Exercise 6 to complete the diagram below.
4x 2
7x
3
4x2 (4x)
, 3 +
4x +
3
,
3
The expressions inside the parentheses must be equal.
Use the Distributive Property to factor out
the GCF, the part inside the parentheses.
+4x 3, +
,
Key Concept Factoring Perfect Square Trinomials
a2 1 2ab 1 b2 5 (a 1 b)2
a2 2 2ab 1 b2 5 (a 2 b)2
x 2 1 2xy 1 y 2
Problem 4
2p2 1 36p 1 9
m2 1 14m 1 72
4s2 1 4s 1 1
Factoring a Perfect Square Trinomial
Got It? What is 64x 2 2 16x 1 1 in factored form?
9. Circle the form your answer will have.
(a 1 b)2
(a 2 b)2
10. Use the justifications to complete each step.
64x 2 2 16x 1 1
Write the original expression.
2
Q
x R 2 16x 1 Q
Q
xR 2 2Q
2
RQ
R
2
Rx 1 Q
Write the first and third terms as squares.
R
2
Write the middle term as (2ac)x.
11. Write the expression as the square of a binomial.
Chapter 4
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8. Circle the polynomials that can be factored as perfect square trinomials.
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Key Concept Factoring a Difference of Two Squares
Aa2 2 b2 B 5 (a 1 b)(a 2 b)
12. Cross out the polynomials that are NOT a difference of two squares.
x2 1 y2
3p2 2 9
36g 2 2 64
w2 2 25x 2
13. Write the missing terms.
4x2 2 81 5 Q 2x 1
Problem 5
RQ
2 9R
5 (m 1 4) Q
m2 2
2 4R
Factoring a Difference of Two Squares
Got It? What is 16x 2 2 81 in factored form?
14. Is each term of the expression a square?
Yes / No
15. Circle the expression with both terms written as squares.
4x 2 9
4x 2 2 92
(4)2x 2 (9)2
(4x)2 2 92
16x 2 2 92
16. The factored form of 16x 2 2 81 is (4x 1 9)(4x 2 9) / (4x 2 9)2 .
Lesson Check • Do you UNDERSTAND?
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Vocabulary Is 4b2 2 26b 1 169 a perfect square trinomial? Explain.
17. The expanded form of (a 2 b)2 is
.
18. Identify the values of the terms a2 , b2 , and 22ab in 4b2 2 26b 1 169.
a2 5 Q
R
2
b2 5 Q
R
2
22ab 5
19. Since the values of a2, b2, and 22ab equal / do not equal the values in the
expression, 4b2 2 26b 1 169 is / is not a perfect square trinomial.
Math Success
Check off the vocabulary words that you understand.
factor of an expression
perfect square trinomial
difference of two squares
Rate how well you can factor quadratic expressions.
Need to
review
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6
8
10
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get it!
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Lesson 4-4, Part 2
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