document.write( "Question 1014361: 3x²-31x-60=0 plz explain me in detail \n" ); document.write( "
Algebra.Com's Answer #630663 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since the leading coefficient 3\r\n" );
document.write( "can only be factored only one way,\r\n" );
document.write( "I think the trial-and-error factoring \r\n" );
document.write( "method is better in this case:\r\n" );
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document.write( "3x²-31x-60=0\r\n" );
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document.write( "Since the last term -60 is negative,\r\n" );
document.write( "we know that the absolute value \r\n" );
document.write( "of the middle coefficient, -31, which\r\n" );
document.write( "is 31, must be the result when the\r\n" );
document.write( "absolute values of the product of the\r\n" );
document.write( "outer and inner terms are subtracted. \r\n" );
document.write( "[If the last term were +, we would \r\n" );
document.write( "know that they would be added].\r\n" );
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document.write( "The factorizations are either of\r\n" );
document.write( "these forms:\r\n" );
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document.write( "(x A)(3x B) \r\n" );
document.write( "(x B)(3x A)\r\n" );
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document.write( "where A and B are as in this chart:\r\n" );
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document.write( "∥ A, B ∥ |B-3A|,|A-3B|\r\n" );
document.write( "∥ 1,60 ∥   57    179\r\n" );
document.write( "∥ 2,30 ∥   24     88\r\n" );
document.write( "∥ 3,20 ∥   11     57\r\n" );
document.write( "∥ 4,15 ∥    3     41\r\n" );
document.write( "∥ 5,12 ∥    3     31\r\n" );
document.write( "∥ 6,10 ∥    8     24\r\n" );
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document.write( "How to make that chart:\r\n" );
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document.write( "In the first column we list all the\r\n" );
document.write( "factor pairs of 60. Then we form\r\n" );
document.write( "the differences mentally, until we\r\n" );
document.write( "come to the absolute value of the\r\n" );
document.write( "coefficient of the middle term, 31. \r\n" );
document.write( "In this case it was the red one.  \r\n" );
document.write( "Often when using this method, we will \r\n" );
document.write( "reach it much sooner, and stop \r\n" );
document.write( "whenever we reach it.\r\n" );
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document.write( "Now since the 31 came from the second\r\n" );
document.write( "column we know that the factorization \r\n" );
document.write( "is of the form:\r\n" );
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document.write( "(x B)(3x A) \r\n" );
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document.write( "so the factorization is \r\n" );
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document.write( "(x 12)(3x 5)\r\n" );
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document.write( "Now the product of the outer terms\r\n" );
document.write( "is 5x and the product of the inner \r\n" );
document.write( "terms is 36x, so to get the middle \r\n" );
document.write( "term -31x, the 36x must be made\r\n" );
document.write( "negative and the 5x must be made \r\n" );
document.write( "positive.  So the factorization is\r\n" );
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document.write( "(x-12)(3x+5).\r\n" );
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document.write( "It takes some practice to use this\r\n" );
document.write( "method, but it'll save time when \r\n" );
document.write( "either the first or last term can \r\n" );
document.write( "be factored only one way.\r\n" );
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document.write( "Edwin
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