document.write( "Question 257298: I have a factoring math problem.******I didn't include the problem on my other one. Here is the corrected math problem question*****************\r
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\n" ); document.write( "\n" ); document.write( "Factoring: Find GCF - Reverse Foil (Quadratic - 2 binomials)\r
\n" ); document.write( "\n" ); document.write( "x^2 + 5x + 6
\n" ); document.write( "My answer is: (x-1)(x+5)\r
\n" ); document.write( "\n" ); document.write( "I don't know about this one.\r
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Algebra.Com's Answer #189217 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
The GCF of $\"x%5E2+%2B+5x+%2B+6\"$ is 1, but it is trivial to factor it out. So we don't have to worry about the GCF.\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2%2B5x%2B6\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"5\"$ , and the last term is $\"6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"6\"$ to get $\"%281%29%286%29=6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"6\"$ (the previous product) and add to the second coefficient $\"5\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"6\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"6\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"6\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*6 = 6
\n" ); document.write( "2*3 = 6
\n" ); document.write( "(-1)*(-6) = 6
\n" ); document.write( "(-2)*(-3) = 6\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"5\"$ :\r
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First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"2\"$ and $\"3\"$ add to $\"5\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"2\"$ and $\"3\"$ both multiply to $\"6\"$ and add to $\"5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"5x\"$ with $\"2x%2B3x\"$ . Remember, $\"2\"$ and $\"3\"$ add to $\"5\"$ . So this shows us that $\"2x%2B3x=5x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%282x%2B3x%29%2B6\"$ Replace the second term $\"5x\"$ with $\"2x%2B3x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B2x%29%2B%283x%2B6%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B2%29%2B%283x%2B6%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B2%29%2B3%28x%2B2%29\"$ Factor out $\"3\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%29%28x%2B2%29\"$ Combine like terms. Or factor out the common term $\"x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B5x%2B6\"$ factors to $\"%28x%2B3%29%28x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2%2B5x%2B6=%28x%2B3%29%28x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B3%29%28x%2B2%29\"$ to get $\"x%5E2%2B5x%2B6\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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