# Factoring Polynomials

 The flashcards below were created by user randycapped on FreezingBlue Flashcards. Greatest Common Factor: The largest number and greatest amount ofvariables that are factors of each term.In other words, we're looking for a number that divides evenly into all values. Identify the GCF among the numbers given using the grouping method: 20, 24 and 100 or  or  or Use the "factor tree" for 100 if needed: Now, look and see all the factors that appear in all three listings: So two factors of 2 are common to all 3 listings. Which gives us the answer: GCF = 22 = 4 Another way to solve this would be to write the product of common prime factors, with each factor raised to the lowest exponent to which it appears. In this example, the only common prime factor is 2. And the smallest exponent to which it appear is the second power. Identify the GCF among the numbers given: 30, 75, 90 15 Identify the GCF: 20x5 - 8x4 + 12x2 GCF = 4x2 20x5 = 8x4  = 12x2 =  Identify the GCF: 18a3b2 - 24a4bc 6a3b 18a3b2 = 2*3*3*a*a*a*b*b 24a4bc = 2*2*2*3*a*a*a*a*b*c Identify the GCF within a binomial: 3x(3y+7) - 4(2y+7) GCF = 2y+7 3x(3y+7) - 4(2y+7) Identify the GCF: GCF = a + b Factor out the GCF: 20x5 - 8x4 + 12x2 Step 1: Find the GCF: 4x2  Step 2: We want to find a product of the GCF            (4x2) and another polynomial that                when multiplied equals the                          original polynomial. Step 3: Use an empty set of parentheses as             a placeholder for three terms: 4x2 (__ - __+__) Step 4: 4x2 times what will give me 20x5 ? 4x2 (5x3 -__ + __) Step 5: 4x2 times what will give me -8x4 ? 4x2 (__ -2x2 + __) Step 6: 4x2 times what will give me 12x2 ?4x2 (__ -__ + 3) Step 7: You can check using multiplication. 4x2 (5x3 -2x2 +3)   = 20x5-8x4 +12x2 Factor out the GCF: Authorrandycapped ID268584 Card SetFactoring Polynomials DescriptionFactoring Polynomials Updated2014-03-31T12:44:11Z Show Answers