Math 017 Materials With Exercises

FactorizationThe Distributive Law lets us change an expression from a product to a sum. When we do that „inreverse‟, the process is called factorization.FactorizationChanging the sum of two or more terms to a product iscalled factorization.When factoring algebraic expressions, we merely rewrite them in a different form. The expressionobtained in the process is equivalent to the original one.Factorization of a common factorConsider 3 A Ax . The expression has two terms: 3 A and Ax . Each has A as its factor. A is acommon factor of both terms. We will factor A from 3 A Ax . 3AAx 3A Ax A A(3 x) A A The first step follows from the Distributive Law. To convince yourself, multiply each term inside 3AAx 3AAxparentheses by A : A A A 3A Ax . The second step is obtained by A A A Acanceling A ‟s . 3 A Ax was originally written as a sum of two terms. By factoring A from 3A + Ax,we are now able to express it in a factored form (that is, as a product of two expressions, rather than asum) 3A Ax A(3 x). Notice that, after factorization, you can always check your answer bymultiplying factors.Example 5.3 Factor2x from the expression3xx5 3 2 2x .Solution:3x5 2x3 x2 x2 3x2 x52x2x3xx22 x2(3x3 2x1)Example 5.4 Factor 2afrom the expression2aa2 3 4a 6 .Solution:2a 4a2 6a32 2a4a 2a 2a2a36a2a 2a(1 2a 3a2)52