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8.5: Factoring using GCF Algebra 1: January 22, 2015 Talk between your neighbors and find the most common piece between the following 1.) 3,9,54 2.) 4x,12 x 2 ,16 x 4 3.) 6 w2 , 24 w4 ,30w5 What do we call the “common piece”? Factoring! • Possible the most important math concept you will see in high school (other than solving) • We will learn multiple ways to factor • Factor means to “un-multiply” • GCF – Greatest common factor: ALWAYS FIRST and we will take out everything we can • We will learn the rest throughout the rest of our chapter • GCF will be like “un-distribute” What a problem looks like… Suggestions: Break it down – numbers first then variables 4 x 12 x 8 x 4 3 2 1.) All terms are divisible by 4 – part of our GCF is 4 4 x 12 x 8 x 4 x 3 x 2 x 4 3 2 4 3 2 2.) All terms have x’s – take our the “most” (the smallest exponent) 4 x 12 x 8 x 4 x 3x 2 x 4 x x 3x 2 4 3 2 4 3 2 2 2 A few together! 6 5 1) 8𝑥 + 4𝑥 + 12𝑥 2 3 2 2) 5𝑐 − 25𝑐 + 10𝑐 Your Turn! 1.) 𝑦 3 – 28𝑦 2 + y 3.) 4𝑎2 b + 28a𝑏 2 + 7ab 2.) 4x + 12𝑥 2 + 16𝑥 3 Factoring to solve • So many ideas in math are to solve – and many of those are when your function = 0 • When a function is factored – set all parts = to 0 • 𝑥 2𝑥 − 3 𝑥 + 1 = 0 gives us 3 solutions • 𝑥 = 0, 2𝑥 − 3 = 0 𝑎𝑛𝑑 𝑥 + 1 = 0 (solve each) See a few in action 1.) 4b(b + 4) = 0 2). (y – 3)(y + 2) = 0 3.) (a + 6)(3a – 7) = 0