document.write( "Question 601655: how do I factor 10x^2-7xy-5y^2 ? \n" ); document.write( "
Algebra.Com's Answer #379930 by Edwin McCravy(20056)\"\" \"About 
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document.write( "10x² - 7xy - 5y²\r\n" );
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document.write( "The factorization, if there is one, has to be of the form\r\n" );
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document.write( "(↏x ↏ ↏y)(↏x ↏ ↏y)\r\n" );
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document.write( "Since there is just one factorization of the number 5 in the \r\n" );
document.write( "last term as 5·1, we can put this:\r\n" );
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document.write( "(↏x ↏ 5y)(↏x ↏ 1y)\r\n" );
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document.write( "The 10 can be factored as 10·1, 5·2, 2·5 and 1·10, so we try all these\r\n" );
document.write( "using tho O and I of \"FOIL\"\r\n" );
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document.write( "(10x ↏ 5y)(1x ↏ 1y) <--- outers = 10xy,  Inners = 5xy, difference = 5xy\r\n" );
document.write( "(5x ↏ 5y)(2x ↏ 1y)  <--- outers = 5xy, Inners = 10xy, difference = 5xy\r\n" );
document.write( "(2x ↏ 5y)(5x ↏ 1y)  <--- outers = 2xy, inners = 25xy, difference = 23xy \r\n" );
document.write( "(1x ↏ 5y)(10x ↏ 1y) <--- outers = 1xy, inners = 50xy, difference = 49xy\r\n" );
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document.write( "Since the last sign of 10x² - 7xy - 5y² is -, we look through\r\n" );
document.write( "those to find one which two have a difference of the middle term,\r\n" );
document.write( "7xy, ignoring the sign.  \r\n" );
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document.write( "There are none, so the trinomial 10x² - 7xy - 5y² is PRIME, i.e., it \r\n" );
document.write( "cannot be factored using integer coefficients.\r\n" );
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document.write( "Edwin
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