document.write( "Question 55229: Please help factor completly\r
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Algebra.Com's Answer #37487 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Please help factor completly \r\n" );
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document.write( "21 + 4x - x²\r\n" );
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document.write( "Put a \"1\" just before the x²\r\n" );
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document.write( "21 + 4x - 1x²\r\n" );
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document.write( "Multiply the 21 by the 1.  You get 21.  Now we\r\n" );
document.write( "ask ourselves this question:\r\n" );
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document.write( "What pair of positive integers have product 21\r\n" );
document.write( "and DIFFERENCE of 4\r\n" );
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document.write( "(I said DIFFERENCE here since the last sign is -. If\r\n" );
document.write( "it had been +, I would have said SUM)\r\n" );
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document.write( "The answer to the question above is the pair 7 and 3.\r\n" );
document.write( "That's because their product is 21 and their \r\n" );
document.write( "difference is 4.\r\n" );
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document.write( "Consider these as representing 7x and 3x.\r\n" );
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document.write( "Now we attach signs to 7x and 3x so that they will\r\n" );
document.write( "combine to the middle term + 4x.  To do that we attach\r\n" );
document.write( "a \"+\" to the 7x and a \"-\" to the 4x, because\r\n" );
document.write( " + 4x = + 7x - 3x\r\n" );
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document.write( "So we replace \"+ 4x\" by \"+ 7x - 3x\", and so,\r\n" );
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document.write( "21 + 4x - 1x² becomes\r\n" );
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document.write( "21 + 7x - 3x - 1x²\r\n" );
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document.write( "Now we factor 7 out of the first two terms, and -1x\r\n" );
document.write( "out of the last two terms:\r\n" );
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document.write( "7(3 + x) - 1x(3 + x)\r\n" );
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document.write( "Now we factor (3 + x) out of both terms\r\n" );
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document.write( "(3 + x)(7 - 1x)\r\n" );
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document.write( "We can erase the 1 and the final answer is\r\n" );
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document.write( "(3 + x)(7 - x)\r\n" );
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document.write( "Edwin
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