document.write( "Question 96009: factor\r
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Algebra.Com's Answer #69911 by Edwin McCravy(20056) $\"\"$ $\"About$

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factor
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document.write( "2x² + 9xy + 10y²\r\n" );
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document.write( "1. Multiply the 2 by the 10, get 20.\r\n" );
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document.write( "2. Notice the sign of the last term is +, so we think \"SUM\".\r\n" );
document.write( "(If the sign of the last term had been -, we would think \"DIFFERENCE\")\r\n" );
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document.write( "3. Think of two positive integers which have product 20 and SUM 9, the\r\n" );
document.write( "coefficient (in absolute value) of the middle term.\r\n" );
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document.write( "It doesn't take long to see that two such positive integers are 5 and 4.\r\n" );
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document.write( "4. Now use 5 and 4 to rewrite the 9 as (5 + 4)\r\n" );
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document.write( "2x² + (5 + 4)xy + 10y²\r\n" );
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document.write( "5. Remove the parentheses by distributing\r\n" );
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document.write( "2x² + 5xy + 4xy + 10y²\r\n" );
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document.write( "6. Factor by grouping. That is,\r\n" );
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document.write( "a. factor the first two terms by taking\r\n" );
document.write( "out x.\r\n" );
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document.write( "b. factor the last two terms by taking out 2y\r\n" );
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document.write( "x(2x + 5y) + 2y(2x + 5y)\r\n" );
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document.write( "c. Now notice that (2x + 5y) is contained in both expressions:\r\n" );
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document.write( "x(2x + 5y) + 2y(2x + 5y)\r\n" );
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document.write( "d. So factor out the whole (2x + 5y) leaving x when factoring\r\n" );
document.write( "it out of the left expression, and leaving 2y when factoring\r\n" );
document.write( "(2x + 5y) out on the right expression.\r\n" );
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document.write( "(2x + 5y)(x + 2y)\r\n" );
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document.write( "That's it!\r\n" );
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document.write( "Edwin

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