Section 5.4Section 5.4

Factoring Quadratic Expressions

Factor each expression.

ALGEBRA 2 LESSON 5-4ALGEBRA 2 LESSON 5-4

Factoring Quadratic ExpressionsFactoring Quadratic Expressions

5-4

Quick Check

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.

Factor each polynomial:3 21. 3 15x x 23x 5x

2 22. 2 4 10x y xy xy

2xy 2 5x y

Factor 100x2 + 180x + 81.

ALGEBRA 2 LESSON 5-4ALGEBRA 2 LESSON 5-4

Factoring Quadratic ExpressionsFactoring Quadratic Expressions

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

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Quick Check

Factor each polynomial:23. 4 4 1m m

24. 10 25b b

25b

Perfect Square TrinomialsPerfect Square Trinomials

2 1 2 1m m

Factor each polynomial:25. 49y

26. 81 4a

9 2 9 2a a

Difference of SquaresDifference of Squares

7 7y y

Factor each polynomial:37. x x 2 1x x

Difference of SquaresDifference of Squares

1 1x x x

Factor each polynomial:28. 5 45mp m 25 9m p

5 3 3m p p

Factor each polynomial.a.

b.Answer:

Answer:

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.

ALGEBRA 2 LESSON 5-4ALGEBRA 2 LESSON 5-4

Factoring Quadratic ExpressionsFactoring Quadratic Expressions

Relate: frame area equals the outer area minus the inner

areaDefine: 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.

5-4

Quick Check

ALGEBRA 2 LESSON 5-4ALGEBRA 2 LESSON 5-4

Factoring Quadratic ExpressionsFactoring Quadratic Expressions

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 + 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)

Factor each expression completely.

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