document.write( "Question 244032: Extremly confused on factoring using the ac-method. Instructions state to factor by grouping.
\n" ); document.write( "The problems are:
\n" ); document.write( "7x(cubed)-15x+2 and 9x(cubed)-6x-8\r
\n" ); document.write( "\n" ); document.write( "I have tried to work out these problems several different ways and can not come to the correct answer.... I believe part of my problem is due to the fact that their are odd numbers and all of my examples have even numbers. Thanks in advance for any help or guidance you can provide me as I am having an extremly difficult time figuring these out. :) \n" ); document.write( "

Algebra.Com's Answer #178642 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Are you sure that the exponents aren't twos? The cubics that you've written out aren't factorable.\r
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\n" ); document.write( "\n" ); document.write( "If the first one is $\"7x%5E2-15x%2B2\"$ , then \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"7x%5E2-15x%2B2\"$ , we can see that the first coefficient is $\"7\"$ , the second coefficient is $\"-15\"$ , and the last term is $\"2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"7\"$ by the last term $\"2\"$ to get $\"%287%29%282%29=14\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"14\"$ (the previous product) and add to the second coefficient $\"-15\"$ ?\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 $\"14\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"14\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-7,-14\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 $\"14\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*14
\n" ); document.write( "2*7
\n" ); document.write( "(-1)*(-14)
\n" ); document.write( "(-2)*(-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 $\"-15\"$ :\r
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First Number	Second Number	Sum
1	14	1+14=15
2	7	2+7=9
-1	-14	-1+(-14)=-15
-2	-7	-2+(-7)=-9

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-1\"$ and $\"-14\"$ add to $\"-15\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-1\"$ and $\"-14\"$ both multiply to $\"14\"$ and add to $\"-15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-15x\"$ with $\"-x-14x\"$ . Remember, $\"-1\"$ and $\"-14\"$ add to $\"-15\"$ . So this shows us that $\"-x-14x=-15x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%5E2%2Bhighlight%28-x-14x%29%2B2\"$ Replace the second term $\"-15x\"$ with $\"-x-14x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%287x%5E2-x%29%2B%28-14x%2B2%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%287x-1%29%2B%28-14x%2B2%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%287x-1%29-2%287x-1%29\"$ Factor out $\"2\"$ 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( " $\"%28x-2%29%287x-1%29\"$ Combine like terms. Or factor out the common term $\"7x-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"7x%5E2-15x%2B2\"$ factors to $\"%28x-2%29%287x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%28x-2%29%287x-1%29\"$ to get $\"7x%5E2-15x%2B2\"$ 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( "As for the other one, let me know if you still need help. \n" ); document.write( "

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