1. Factoring Quadratic Expressions
Section 5.4
Factoring Quadratic Expressions

2. Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
Factor each expression.
a. 15x2 + 25x + 100
15x2 + 25x = 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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3. Factor each polynomial:

4. Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
Factor 100x x + 81.
100x x + 81 = (10x) (9)2 Rewrite the first and third terms as squares.
= (10x) (9)2 Rewrite the middle term to verify the perfect square trinomial pattern.
= (10x + 9)2 a2 + 2ab + b2 = (a + b)2
Quick Check
5-4

5. Perfect Square Trinomials
Factor each polynomial:

6. Factor each polynomial:
Difference of Squares
Factor each polynomial:

7. Factor each polynomial:
Difference of Squares
Factor each polynomial:

8. Factor each polynomial:

9. Factor each polynomial. a.b.
Answer:
Answer:

10. 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.
Relate: frame area equals the outer area minus the inner area
Define: Let x = length of side of frame.
Write: area = x2 – (7)2
= (x + 7)(x – 7)
The area of the frame in factored form is (x + 7)(x – 7) in2.
Quick Check
5-4

11. Factoring Quadratic Expressions
ALGEBRA 2 LESSON 5-4
Factor each expression completely.
1. 12x2 + 6x m2 + 11m + 18
3. x2 – 14x – x2 – 13x + 42
5. 64x x x2 + 5x – 50
7. 5k2 – n2 – 8n + 1
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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