document.write( "Question 1073812: I need to factor the polynomial $\"x%5E2%2B13x%2B12\"$ \n" ); document.write( "

Algebra.Com's Answer #688594 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "See the 12 on the right end?\r\n" );
document.write( "See the + sign before the 12?  \r\n" );
document.write( "See the 13 in the middle?\r\n" );
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document.write( "Think of two positive integers that when multiplied give 12,\r\n" );
document.write( "but when ADDED (because the sign of 12 is +) gives 13.\r\n" );
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document.write( "We think of 12 and 1 because 12×1=12 and 12+1=13\r\n" );
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document.write( "S we write this\r\n" );
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document.write( "(x 12)(x 1)\r\n" );
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document.write( "Now since the sign of 12 is +, the signs will both be\r\n" );
document.write( "the same.  What sign? We look at the sign in the middle,\r\n" );
document.write( "the sign of 13.  It is +, so we put +'s in both parentheses:\r\n" );
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document.write( "(x+12)(x+1)\r\n" );
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document.write( "That's it.\r\n" );
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document.write( "We check by FOIL and get\r\n" );
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document.write( "x²+x+12x+12\r\n" );
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document.write( "which simplifies to:\r\n" );
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document.write( "x²+13x+12\r\n" );
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document.write( "So it checks.\r\n" );
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document.write( "Answer: (x+12)(x+1)\r\n" );
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document.write( "Edwin

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