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January 26, 2016 Lesson 6.1 Greatest Common Factor and Factoring by Grouping List all possible factors of 105. 1,, 3,, 5,, 7,, 15,, 21,, 35,, 105. To find the GCF of a set of numbers 1. Write the prime factorization of each in exponential form. 2. Collect only those prime factors common to all the numbers in the set, each raised to the smallest exponent in the factorizations. 3. Multiply this result. Find the GCF of 248 and 316. 2 248 2 124 2 62 31 3 248 = 2 •31 2 316 2 158 79 2 316 = 2 •79 2 GCF iss 2 = 4 To factor a monomial GCF out of a given polynomial, 1. Find the GCF of the terms in the polynomial. 2. Rewrite the polynomial as a product of the GCF and the quotient of the polynomial and the GCF. 1 January 26, 2016 Factor . What is the GCF of the terms in the 2 polynomial? 6xy Factor 1. Determine the GCF of the terms in the polynomial. 2. Divide the polynomial by the GCF and write the factorization. 2 January 26, 2016 Lesson 6.1 pages 423-424 even answers. 3 January 26, 2016 4 January 26, 2016 Factoring by Grouping. To factor a four-term polynomial by grouping, 1. Factor out any monomial GCF that is common to all four terms. 2. Group pairs of terms and factor the GCF out of each pair. 3. If there is a common binomial factor, factor it out. 4. If there is no common binomial factor, interchange the middle two terms and repeat the process. If there is still no common binomial factor, this method of grouping will not work. Factor = 4n(3mn - 5m - 6n + 10) = 4n[m(3n - 5) - 2(3n - 5)] = 4n (3n - 5)(m - 2) Now you try factoring 5 January 26, 2016 More examples. 6