document.write( "Question 197636: factor out this problem.
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\n" ); document.write( "x^2+11x+28
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\n" ); document.write( "thank you \n" ); document.write( "

Algebra.Com's Answer #148199 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2%2B11x%2B28\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"11\"$ , and the last term is $\"28\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"28\"$ to get $\"%281%29%2828%29=28\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"28\"$ (the previous product) and add to the second coefficient $\"11\"$ ?\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 $\"28\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"28\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,7,14,28\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-7,-14,-28\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 $\"28\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*28
\n" ); document.write( "2*14
\n" ); document.write( "4*7
\n" ); document.write( "(-1)*(-28)
\n" ); document.write( "(-2)*(-14)
\n" ); document.write( "(-4)*(-7)\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 $\"11\"$ :\r
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First Number	Second Number	Sum
1	28	1+28=29
2	14	2+14=16
4	7	4+7=11
-1	-28	-1+(-28)=-29
-2	-14	-2+(-14)=-16
-4	-7	-4+(-7)=-11

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"4\"$ and $\"7\"$ add to $\"11\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"4\"$ and $\"7\"$ both multiply to $\"28\"$ and add to $\"11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"11x\"$ with $\"4x%2B7x\"$ . Remember, $\"4\"$ and $\"7\"$ add to $\"11\"$ . So this shows us that $\"4x%2B7x=11x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%284x%2B7x%29%2B28\"$ Replace the second term $\"11x\"$ with $\"4x%2B7x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B4x%29%2B%287x%2B28%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B4%29%2B%287x%2B28%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B4%29%2B7%28x%2B4%29\"$ Factor out $\"7\"$ 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( " $\"%28x%2B7%29%28x%2B4%29\"$ Combine like terms. Or factor out the common term $\"x%2B4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B11x%2B28\"$ factors to $\"%28x%2B7%29%28x%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%28x%2B7%29%28x%2B4%29\"$ to get $\"x%5E2%2B11x%2B28\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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