document.write( "Question 157262This question is from textbook algebra 2
\n" ); document.write( ": Please help me solve this problem 6c^2+13c+6 \n" ); document.write( "

Algebra.Com's Answer #115903 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that you want to factor. \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"6c%5E2%2B13c%2B6\"$ , we can see that the first coefficient is $\"6\"$ , the second coefficient is $\"13\"$ , and the last term is $\"6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"6\"$ by the last term $\"6\"$ to get $\"%286%29%286%29=36\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"36\"$ (the previous product) and add to the second coefficient $\"13\"$ ?\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 $\"36\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"36\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,9,12,18,36\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-9,-12,-18,-36\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 $\"36\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*36
\n" ); document.write( "2*18
\n" ); document.write( "3*12
\n" ); document.write( "4*9
\n" ); document.write( "6*6
\n" ); document.write( "(-1)*(-36)
\n" ); document.write( "(-2)*(-18)
\n" ); document.write( "(-3)*(-12)
\n" ); document.write( "(-4)*(-9)
\n" ); document.write( "(-6)*(-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 $\"13\"$ :\r
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First Number	Second Number	Sum
1	36	1+36=37
2	18	2+18=20
3	12	3+12=15
4	9	4+9=13
6	6	6+6=12
-1	-36	-1+(-36)=-37
-2	-18	-2+(-18)=-20
-3	-12	-3+(-12)=-15
-4	-9	-4+(-9)=-13
-6	-6	-6+(-6)=-12

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"4\"$ and $\"9\"$ add to $\"13\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"4\"$ and $\"9\"$ both multiply to $\"36\"$ and add to $\"13\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"13c\"$ with $\"4c%2B9c\"$ . Remember, $\"4\"$ and $\"9\"$ add to $\"13\"$ . So this shows us that $\"4c%2B9c=13c\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"6c%5E2%2Bhighlight%284c%2B9c%29%2B6\"$ Replace the second term $\"13c\"$ with $\"4c%2B9c\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%286c%5E2%2B4c%29%2B%289c%2B6%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"2c%283c%2B2%29%2B%289c%2B6%29\"$ Factor out the GCF $\"2c\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"2c%283c%2B2%29%2B3%283c%2B2%29\"$ 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( " $\"%282c%2B3%29%283c%2B2%29\"$ Combine like terms. Or factor out the common term $\"3c%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"6c%5E2%2B13c%2B6\"$ factors to $\"%282c%2B3%29%283c%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%282c%2B3%29%283c%2B2%29\"$ to get $\"6c%5E2%2B13c%2B6\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "\n" ); document.write( "Questions? Email me at jim_thompson5910@hotmail.com \n" ); document.write( "

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