10-2 Factoring Using the Distributive Property

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Factoring Using the Distributive Property.

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10-2 Factoring Using the Distributive Property Objectives 1. factor polynomials using the Distributive Property. 2. solve quadratic equations of the form ax2 + bx = 0. Designed by Skip Tyler, Varina High School

Review: What is the GCF of 25a2 and 15a? Let’s go one step further… 1) FACTOR 25a2 + 15a. Find the GCF and divide each term 25a2 + 15a = 5a( ___ + ___ ) Check your answer by distributing. 5a 3

2) Factor 18x2 - 12x3. Find the GCF 6x2 Divide each term by the GCF 18x2 - 12x3 = 6x2( ___ - ___ ) Check your answer by distributing. 3 2x

3) Factor 28a2b + 56abc2. GCF = 28ab Divide each term by the GCF 28a2b + 56abc2 = 28ab ( ___ + ___ ) Check your answer by distributing. 28ab(a + 2c2) a 2c2

Factor 20x2 - 24xy x(20 – 24y) 2x(10x – 12y) 4(5x2 – 6xy) 4x(5x – 6y)

5) Factor 28a2 + 21b - 35b2c2 GCF = 7 Divide each term by the GCF Check your answer by distributing. 7(4a2 + 3b – 5b2c2) 4a2 3b 5b2c2

Factor 16xy2 - 24y2z + 40y2 2y2(8x – 12z + 20) 4y2(4x – 6z + 10) 8xy2z(2 – 3 + 5)

Video—Factoring Using the GCF http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-267s.html

What happens if your polynomial has 4 terms?

Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more 2. Grouping 4

1. Factor 12ac + 21ad + 8bc + 14bd Do you have a GCF for all 4 terms? Group the first 2 terms and the last 2 terms. 12ac + 21ad + 8bc + 14bd Find the GCF of each group. 3a (4c + 7d) + 2b(4c + 7d) The parentheses are the same! (3a + 2b)(4c + 7d) No

2. Factor rx + 2ry + kx + 2ky Check for a GCF: None You have 4 terms - try factoring by grouping. rx + 2ry + kx + 2ky Find the GCF of each group. r(x + 2y) + k(x + 2y) The parentheses are the same! (r + k)(x + 2y)

3. Factor 2x2 - 3xz - 2xy + 3yz Check for a GCF: None Factor by grouping. 2x2 - 3xz - 2xy + 3yz Find the GCF of each group. x(2x - 3x) - y(2x - 3z) Pay close attention to the signs in the second set of parentheses. The parentheses are the same! (x - y)(2x - 3z)

4. Factor 16k3 - 4k2p2 - 28kp + 7p3 Check for a GCF: None Factor by grouping. 16k3 - 4k2p2 - 28kp + 7p3 Find the GCF of each group. 4k2(4k - p2) - 7p(4k - p2) The signs are opposite in the parentheses! (4k2 - 7p)(4k - p2)