Example 11 - factors x 2 xy 2 y = x xy 2 2 y Grouping gives x xy(2 2 y Now factoring gives x(1 y 2(1 y Using the distributive property gives x 2(1

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Example 11 Factor 3  x 2  – 48.  Factoring out a 3 leaves 3(  x 2  – 16)  But  x 2  – 16 is the difference between two squares and can be further factored into (  x  + 4)(  x  – 4).  Therefore, when completely factored, 3  x 2  – 48 = 3(  x  + 4)(  x  – 4).  Factoring by grouping Some polynomials have binomial, trinomial, and other polynomial factors. Example 12 Factor  x  + 2 +  xy  + 2  y Since there is no monomial factor, you should attempt rearranging the terms and looking for binomial 
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Unformatted text preview: factors. x + 2 + xy + 2 y = x + xy + 2 + 2 y Grouping gives ( x + xy ) + (2 + 2 y ) Now factoring gives x (1 + y ) + 2(1 + y ) Using the distributive property gives ( x + 2)(1 + y ) You could rearrange them differently, but you would still come up with the same factoring....
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This note was uploaded on 11/09/2011 for the course MATH 1310 taught by Professor Staff during the Fall '07 term at Texas State.

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