Download Lesson 6.1 1, 3, 5, 7, 15, 21, 35, 105. 124 62 248 31 2 2 2 158 79 2

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.
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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.
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Lesson 6.1 pages 423-424 even answers.
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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
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More examples.
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