Factoring Polynomials- Step by Step Guide

Aug 16th, 2016
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This document describes how to factor polynomials using the following methods. 1. Greatest Common Factor 2. Grouping 3. Trinomials 4. Difference of Squares A detailed explanations are given and answers are explained for all the practice problems.

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Algebra FactoringStep by Step GuideSasanthi Peiris 2016All Rights ReservedContentsGreatest Common Factor (GCF)GroupingQuadratic TrinomialsDifference of two perfect squaresFactoringFactoring can be categorized into following methods. Common Factor (GCF)GroupingQuadratic Trinomials in the form of ax2 bx cDifference of two perfect squares1. Greatest Common Factor (GCF)GCF is the common term for all the terms in an expression.GCF of numbers: The largest number that goes into all the numbers in the expression.Examples:The GCF of 4, 6 and 8 is 2The GCF of 8, 12 and 20 is 4The GCF of 12, 15 ad 21 is 3GCF of letters/variables: First, find the common variables for all the terms. Then for each commonvariable the GCF will be the one with the lowest exponent.Examples:The GCF of xy 2 , xy is xyThe GCF of x 2 y 2 , x 2 y is x 2 yThe GCF of x3 y 2 z, xy 2 z 2 , x 2 y 3 is xy 2 (in this example z is not common for all the terms)IMPORTANT: When solving a factoring question always check for the GCF first.Now lets see some examples.Steps to solve using GCF method1. Find the GCF2. Factor out the GCF and divide the each and every term in the question by the GCF3. Use the laws of exponents when dividingxm x mnnxExamples:x3 x 3 2 x2xx2 x 22 x 0 12xx5 x 51 x 4xx x11 x0 1xx3 y x32 y11 x1 y 0 x1 1 x

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