mac1140_lecture3_2 - L3 1.4 Factoring Factoring out a 1:...

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20L3§1.4 FactoringFactoring– the process of finding polynomials whoseproduct is equal to a given polynomial.A polynomial is considered to befactored completelyifit is written as a product ofprimeorirreduciblepolynomials.Factoring out theGCF(Greatest Common Factor):Use the distributive property to factor out the GCF.The GCF is the product of the largest common factorof all numbers and all common factors containingvariables, each with the smallest exponentthat appearson that factor.Example. Factor out the GCF from each polynomial:a)53986x yxy+b)2325(2)(2)xxx x+21Factoring out a1:Example. Use the distributive property to simplify:2(234)xx+=By using the distributive property, we can factor a1out of a polynomial by changing the sign of each term.Example.Factor a1out of each polynomial:a)2xb)2345xx+Factoring by grouping:Sometimes this method works when we have apolynomial with more than 3 terms. To apply, collect

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