document.write( "Question 258816: I need help with this problem factoring it completely:\r
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Algebra.Com's Answer #190541 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "\"-4x%5E2+%2B+23x+-+28\"\r\n" );
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document.write( "First factor out a -1\r\n" );
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document.write( "\"-%28red%284%29x%5E2-23x%2Bred%2828%29%29\"\r\n" );
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document.write( "Multiply the \"red%284%29\" by the \"red%2828%29\"\r\n" );
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document.write( "Get 112.\r\n" );
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document.write( "Write down all the ways to break 112 into 2 factors of whole numbers\r\n" );
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document.write( "112x1\r\n" );
document.write( " 56x2\r\n" );
document.write( " 28x4\r\n" );
document.write( " 16x7\r\n" );
document.write( " 14x8\r\n" );
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document.write( "Notice that the last sign is a plus:\r\n" );
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document.write( "\"%22-%28%22\"\"4x%5E2-23x\"\"red%28%22%2B%22%29\"\"28%29\"\r\n" );
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document.write( "Plus means add so beside those numbers we\r\n" );
document.write( "just multiplied, let's add them:\r\n" );
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document.write( "112x1  112+1=113\r\n" );
document.write( " 56x2   56+2=58 \r\n" );
document.write( " 28x4   28+4=32\r\n" );
document.write( " 16x7   16+7=23\r\n" );
document.write( " 14x8   14+8=22\r\n" );
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document.write( "Look at the middle term of\r\n" );
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document.write( "\"-%284x%5E2-red%2823%29x%2B28%29\"\r\n" );
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document.write( "in absolute value.  It is a 23.  Now \r\n" );
document.write( "look among those sums we just found.  \r\n" );
document.write( "Is there a 23 among them?  Yes.  That\r\n" );
document.write( "means it can be factored. We find:\r\n" );
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document.write( " 16x7   16+7=23\r\n" );
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document.write( "So let's replace 23 by \"red%28%2816%2B7%29%29\"\r\n" );
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document.write( "\"-%284x%5E2-red%28%2816%2B7%29%29x%2B28%29\"\r\n" );
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document.write( "Now distribute it out\r\n" );
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document.write( "\"-%284x%5E2-16x-7x%2B28%29\"\r\n" );
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document.write( "Factor 4x out of the first two terms:\r\n" );
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document.write( "\"-%284x%28x-4%29-7x%2B28%29\"\r\n" );
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document.write( "Factor -7 out of the last two terms:\r\n" );
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document.write( "\"-%284x%28x-4%29-7%28x-4%29%29\"\r\n" );
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document.write( "Notice the common factor \"green%28%28x-4%29%29%29\"\r\n" );
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document.write( "\"-%284x%2Agreen%28%28x-4%29%29-7%2Agreen%28%28x-4%29%29%29\"\r\n" );
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document.write( "Factor out the green \"green%28%28x-4%29%29\"\r\n" );
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document.write( "\"-%28green%28%28x-4%29%29%284x-7%29%29\"\r\n" );
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document.write( "We can now remove the outer parentheses but leave\r\n" );
document.write( "the negative sign in front:\r\n" );
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document.write( "\"-%28x-4%29%284x-7%29\"\r\n" );
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document.write( "Edwin
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