Sec-41 - Math 1300 Section 4.1 Notes Greatest Common Factor...

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Math 1300 Section 4.1 Notes 1 Greatest Common Factor and Factoring by Grouping (Review) Factoring Definition: A factor is a number, variable, monomial, or polynomial which is multiplies by another number, variable, monomial, or polynomial to obtain a product. 1. List all the possible factors of the following numbers: a. 12 b. 32 c. 19 d. -45 In the above, the number 19 is an example of a ____________ number because its only positive factors are one and itself . (Review) Greatest Common Factor Definition: The greatest common factor of two or more numbers is the largest number that divides (goes into) the given numbers with a remainder of zero. 2. Find the GCF (greatest common factor) of the following numbers: a. 36 and 54 b. 15 and 60 c. 21, 42, and 63 d. 28 and 39
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Math 1300 Section 4.1 Notes 2 Greatest Common Factor of Polynomials In order to find the GCF of two or more monomials, I. Find the GCF of the coefficients; II. Find the GCF of the variables; III. Rewrite the GCF as a product of the GCF of the coefficients times the GCF of the variables. Examples: 1. Find the GCF of x 4 and x 7 . Step I: The only coefficients are 1’s, so this is the GCF of the coefficients. Step II: Rewrite the two monomials as products of x s without using exponents: x 4 = x · x · x · x x 7 = x · x · x · x · x · x · x Since each monomial has 4 x s in it, the GCF of the variables is x 4 .
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