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Learn about factors, GCF, factoring, and practice problems with step-by-step examples in algebraic expressions. Enhance your skills to factor out GCF and factor by grouping effectively.
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Unit 2: FactoringPart 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 ofx3: 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 GCFThis 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 • 2a + 2b + 2c • 3xy – 4xy2 + 5x2y3 • 7x2 + 21x + 14
A few more… x + 3 = x( ) + 3( ) = x(x – 2) + 3(x – 2) =
Factor by GroupingThis 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 • 4x3 + 2x2 – 6x – 3 • 3xy + 21x - 2y – 14
Factoring Trinomials • Factoring by Grouping STEPS: 1. Multiply the first and last term. • Identify the coefficient of the x term. • 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). • Rewrite the original problem, replacing the middle term with the numbers from Step 3. • Factor by grouping.
