document.write( "Question 104536: Please help me factor the following:
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Algebra.Com's Answer #76064 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Please help me factor the following:
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document.write( "6x²-7x-3\r\n" );
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document.write( "Multiply the green 6 times the red -3.\r\n" );
document.write( "That gives -18.\r\n" );
document.write( "Think of two integers which have\r\n" );
document.write( "   1. Product = -18\r\n" );
document.write( "   2. Sum = the blue -7\r\n" );
document.write( "Such a pair of integers are -9 and +2\r\n" );
document.write( "because \r\n" );
document.write( "   1. Product = (-9)x(+2) = -18 \r\n" );
document.write( "   2. Sum =     (-9)+(+2) = -7\r\n" );
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document.write( "Replace the middle term -7x by -9x + 2x, using \r\n" );
document.write( "the -9 and the +2 as coefficients of x.\r\n" );
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document.write( "6x² - 9x + 2x - 3\r\n" );
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document.write( "Factor the first two terms by taking out GCF 3x\r\n" );
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document.write( "  6x² - 9x + 2x - 3\r\n" );
document.write( "3x(2x - 3) + 2x - 3\r\n" );
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document.write( "Factor the last two terms by taking out GCF = +1\r\n" );
document.write( "(When there is nothing bigger that can be factored out,\r\n" );
document.write( "then factor out +1 if the next to last term is \r\n" );
document.write( "positive, or -1 if it is negative.)\r\n" );
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document.write( "3x(2x - 3) + 2x - 3\r\n" );
document.write( "3x(2x - 3) + 1(2x - 3)\r\n" );
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document.write( "Now notice that the red expression (2x - 3) appears\r\n" );
document.write( "in both terms as shown by the colors below:\r\n" );
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document.write( "3x(2x - 3) + 1(2x - 3)\r\n" );
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document.write( "So factor out the red expression (2x - 3) and\r\n" );
document.write( "place the black parts inside parentheses:\r\n" );
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document.write( "3x(2x - 3) + 1(2x - 3)\r\n" );
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document.write( "(2x - 3)(3x + 1)\r\n" );
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document.write( "That's it, and you can just make it all black:\r\n" );
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document.write( "(2x - 3)(3x + 1)\r\n" );
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document.write( "------------------------------------------------\r\n" );
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document.write( "That's the answer. You can check it by FOIL:\r\n" );
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document.write( "          6x² + 2x - 9x - 3\r\n" );
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document.write( "and combining the middle two terms:\r\n" );
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document.write( "          6x² - 7x - 3\r\n" );
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document.write( "which is what we started with, so \r\n" );
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document.write( "(2x - 3)(3x + 1) is the correct factorization.\r\n" );
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document.write( "Edwin

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