Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Unit 2: Factoring Part I MM 218 McGrath Vocubulary • A factor is a number, variable, or algebraic expression multiplying another number, variable or algebraic expression. Example: 4*3 (both the “4” and the “3” are factors) Example: 2x*3y2 (both the “2x” and the “3y2” are factors) Vocabulary • A greatest common factor (GCF) is the largest factor common to 2 or more terms Example: Find the GCF of 12 and 18 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 Common Factors: 1, 2, 3, 6 Greatest Common Factor: 6 GCF Cont’d • Example: Find the GCF of 6x3 and 15x2 Factors of 6 : 1, 2, 3, 6 Factors of x3: x*x*x Factors of 15: 1, 3, 5, 15 Factors of x2: x*x Common Factors: 1, 3, 6, x*x Greatest Common Factor: 6x2 Factoring out a GCF This is distribution in reverse! Distribute: 2(x + 3) = 2(x) + 2(3) = 2x + 6 Factoring: 2x + 6 = 2(x) + 2(3) = 2(x + 3) Factoring out the GCF • Factor: 3x – 12 • Factor 12y2 – 5y Factoring out the GCF Factor: 4x2y3 + 10x5y - 6x3y2 Practice with GCFs 1. 2a + 2b + 2c 2. 3xy – 4xy2 + 5x2y3 3. 7x2 + 21x + 14 A few more… x +3 x( ) + 3( = )= x(x – 2) + 3(x – 2) = Factor by Grouping This is the same as doing the GCF, but now we do it THREE times! • Factor x(z + w) + 2(z + w) • Example: Factor ad + 3a – d2 – 3d • Solution: ad + 3a – d2 – 3d = ad – d2 + 3a – 3d = = d(a – d) + 3(a – d) = = (a – d)(d + 3) Practice with Factoring by Grouping 1. 4x3 + 2x2 – 6x – 3 2. 3xy + 21x - 2y – 14 Factoring Trinomials • Factoring by Grouping STEPS: 1. Multiply the first and last term. 2. Identify the coefficient of the x term. 3. Find two numbers that MULTIPLY to the product of the first and last term (Step 1) and ADD to the coefficient of the x term (Step 2). 4. Rewrite the original problem, replacing the middle term with the numbers from Step 3. 5. Factor by grouping. Example Factor: 10a2 – a – 2 Steps We need to find two numbers that: 1) multiply to -20; and 2) add to -1 The only two numbers that work are -5 and +4. =10a2 – 5a + 4a – 2 Rewrite the equation by substituting the new values in for the middle term. =5a(2a – 1) + 2(2a – 1) Factor by grouping. =(2a – 1)(5a + 2) Factor: x2 – 12x + 32 Factor: 3x2 – 6x + 3 Factor: 4x2 – 14x – 30