document.write( "Question 485408: how do you factor 2x^2+9x-5
\n" ); document.write( "i have a summer math packet and im SO CONFUSED on factoring. please and thank you. \n" ); document.write( "
Algebra.Com's Answer #331986 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There are two methods.  The trial and error method and the \"ac\"-method.\r\n" );
document.write( "When a trinomial starts or ends with a prime number or 1, the trial and\r\n" );
document.write( "error method is easier.  In your problem both 2 and 5 are prime, so\r\n" );
document.write( "the trial-and-error method is easier.  I'll show it here.  However,\r\n" );
document.write( "if you want to learn the ac-method, go here:\r\n" );
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document.write( "http://www.algebra.com/my/change_this_name32371.lesson?content_action=show_dev\r\n" );
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document.write( "Factor 2x²+9x-5\r\n" );
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document.write( "It's the reverse of FOIL\r\n" );
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document.write( "The first coefficient is 2.\r\n" );
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document.write( "The only way to factor that first coefficient, 2, is as 2·1\r\n" );
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document.write( "The constant (ignoring signs) is 5.\r\n" );
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document.write( "The only way to factor 5 is  as 5·1\r\n" );
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document.write( "So the incomplete factorization without the signs \r\n" );
document.write( "has to be one of these two:\r\n" );
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document.write( "(2x   5)(x   1)  or  (2x   1)(x   5)\r\n" );
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document.write( "-----\r\n" );
document.write( "For (2x  5)(x   1), if we used FOIL, the OUTERS and INNERS\r\n" );
document.write( "would be 2x and 5x, but there is NO way to assign signs\r\n" );
document.write( "to them so that when they are combined they would give \r\n" );
document.write( "the middle term +9x.  So that is not the right form.\r\n" );
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document.write( "For (2x  1)(x   5), if we used FOIL the OUTERS and INNERS\r\n" );
document.write( "would be 10x and 1x, and there IS a way to assign signs\r\n" );
document.write( "to them so that when they are combined they would give \r\n" );
document.write( "the middle term +9x.  So we have to assign the 10x a +\r\n" );
document.write( "sign and the 1x a - sign.  The 10x comes from the OUTERS\r\n" );
document.write( "so we put a + before the 5, and we put a - sign before \r\n" );
document.write( "the 1:\r\n" );
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document.write( "Answer:  (2x - 1)(x + 5)\r\n" );
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document.write( "Check by multiplying it out by FOIL:\r\n" );
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document.write( "     2x² + 10x - 1x - 5\r\n" );
document.write( "       2x² + 9x - 5\r\n" );
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document.write( "That's the original trinomial, so we are correct.\r\n" );
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document.write( "Edwin
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