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Section 5.4

Section 5.4. Factoring Quadratic Expressions. Factoring Quadratic Expressions. ALGEBRA 2 LESSON 5-4. Factor each expression. a. 15 x 2 + 25 x + 100 . 15 x 2 + 25 x + 100 = 5(3 x 2 ) + 5(5 x ) + 5(20) Factor out the GCF, 5.

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Section 5.4

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  1. Section 5.4 Factoring Quadratic Expressions

  2. 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

  3. Factor each polynomial:

  4. Factoring Quadratic Expressions ALGEBRA 2 LESSON 5-4 Factor 100x2 + 180x + 81. 100x2 + 180x + 81 = (10x)2 + 180 + (9)2Rewrite the first and third terms as squares. = (10x)2 + 180 + (9)2Rewrite the middle term to verify the perfect square trinomial pattern. = (10x + 9)2a2 + 2ab + b2 = (a + b)2 Quick Check 5-4

  5. Perfect Square Trinomials Factor each polynomial:

  6. Difference of Squares Factor each polynomial:

  7. Difference of Squares Factor each polynomial:

  8. Factor each polynomial:

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

  10. Relate: frame area equals the outer area minus the inner area Write: area = x2 – (7)2 = (x + 7)(x – 7) 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 5-4

  11. 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

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