document.write( "Question 190939: Please help me with this question 3n(squared) + 2n - 1. Thank You \n" ); document.write( "

Algebra.Com's Answer #143354 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming you want to factor?\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3n%5E2%2B2n-1\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"2\"$ , and the last term is $\"-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-1\"$ to get $\"%283%29%28-1%29=-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-3\"$ (the previous product) and add to the second coefficient $\"2\"$ ?\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 $\"-3\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-3\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-3\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 $\"-3\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-3)
\n" ); document.write( "(-1)*(3)\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 $\"2\"$ :\r
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First Number	Second Number	Sum
1	-3	1+(-3)=-2
-1	3	-1+3=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-1\"$ and $\"3\"$ add to $\"2\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-1\"$ and $\"3\"$ both multiply to $\"-3\"$ and add to $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"2n\"$ with $\"-n%2B3n\"$ . Remember, $\"-1\"$ and $\"3\"$ add to $\"2\"$ . So this shows us that $\"-n%2B3n=2n\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3n%5E2%2Bhighlight%28-n%2B3n%29-1\"$ Replace the second term $\"2n\"$ with $\"-n%2B3n\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283n%5E2-n%29%2B%283n-1%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"n%283n-1%29%2B%283n-1%29\"$ Factor out the GCF $\"n\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"n%283n-1%29%2B1%283n-1%29\"$ Factor out $\"1\"$ 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( " $\"%28n%2B1%29%283n-1%29\"$ Combine like terms. Or factor out the common term $\"3n-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"3n%5E2%2B2n-1\"$ factors to $\"%28n%2B1%29%283n-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%28n%2B1%29%283n-1%29\"$ to get $\"3n%5E2%2B2n-1\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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