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**Unformatted text preview: **Supplementary Course Module B: Algebraic Expressions Assignment 3 & Factoring Factoring: & Factoring can be thought of as the &opposite¡ of distributing. & For example, 5 a (2 b + 3 c ) = 10 ab + 15 ac by use of the distributive law, while 10 ab + 15 ac = 5 a (2 b + 3 c ) by a process called factorization. Common Factoring: & To find a common factor: & Determine the largest number that divides evenly into all coefficients. & Determine which variables are common to all terms. & Together, 1 ¡ 2 form the &common factor¡. & Rewrite the original expression enclosed in brackets. The common factor is the multiple outside of the brackets. Divide each of the original terms by the common factor to get the resulting expression inside of the brackets. examples: 6 x ¢ 10 = 2 & 6 x 2 ¢ 10 2 ¡ = 2 (3 x ¢ 5) 12 a 2 bc ¢ 8 ab 2 c + 4 abc = 4 abc (3 a ¢ 2 b + 1) & Common factoring is an important technique used when simplifying derivatives in calculus, in particular when the derivative has been determined by use of the chain rule along with either the product or quotient rule. The following example starts with an expression that could represent such a derivative.following example starts with an expression that could represent such a derivative....

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