Factoring Quadratic Expressions

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Factoring Quadratic Expressions

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Factoring Quadratic Expressions Section 5.4 Factoring Quadratic Expressions

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 5-4

Factor each polynomial:

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 5-4

Perfect Square Trinomials Factor each polynomial:

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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. 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

Factoring Quadratic Expressions ALGEBRA 2 LESSON 5-4 Factor each expression completely. 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) 5-4