Factoring Quadratic Expressions

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Section 5.4

• Factoring Quadratic Expressions

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Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
Factor each expression.
a. 15x2 25x 100
15x2 25x 100 5(3x2) 5(5x) 5(20) Factor
out the GCF, 5
5(3x2 5x 20) Rewrite using the
Distributive Property.
b. 8m2 4m
8m2 4m 4m(2m) 4m(1) Factor out the GCF, 4m
4m(2m 1) Rewrite using the Distributive
Property.
Quick Check
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Factor each polynomial
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Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
Factor 100x2 180x 81.
100x2 180x 81 (10x)2 180 (9)2 Rewrite
the first and third terms as squares.
(10x)2 180 (9)2 Rewrite the middle term to
verify the perfect square trinomial pattern.
(10x 9)2 a2 2ab b2 (a b)2
Quick Check
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Perfect Square Trinomials
Factor each polynomial
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Difference of Squares
Factor each polynomial
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Difference of Squares
Factor each polynomial
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Factor each polynomial
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Factor each polynomial.a. b.
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Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
A square photo is enclosed in a square frame, as
shown in the diagram. Express the area of the
frame (the shaded area) in completely factored
form.
Define Let x length of side of frame.
The area of the frame in factored form is (x
7)(x 7) in2.
Quick Check
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Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
1. 12x2 6x 18 2. m2 11m 18 3. x2
14x 15 4. x2 13x 42 5. 64x2 144x
81 6. 3x2 5x 50 7. 5k2 125 8. 15n2 8n
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Factor each expression completely.
6(2x2 x 3)
(m 2)(m 9)
(x 15)(x 1)
(x 6)(x 7)
(8x 9)2
(3x 10)(x 5)
5(k 5)(k 5)
(5n 1)(3n 1)
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