document.write( "Question 703839: Can you help me factor this equation?
\n" ); document.write( "2x^2+5x+3.
\n" ); document.write( "ac=6
\n" ); document.write( "b=5
\n" ); document.write( "I'm guessing the factors are 2 and 3? Can you please confirm if I am right?
\n" ); document.write( "Thank you so much! \n" ); document.write( "

Algebra.Com's Answer #433728 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 $\"2x%5E2%2B5x%2B3\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"5\"$ , and the last term is $\"3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"3\"$ to get $\"%282%29%283%29=6\"$ .\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( " $\"2x%5E2%2Bhighlight%282x%2B3x%29%2B3\"$ Replace the second term $\"5x\"$ with $\"2x%2B3x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2%2B2x%29%2B%283x%2B3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%28x%2B1%29%2B%283x%2B3%29\"$ Factor out the GCF $\"2x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%28x%2B1%29%2B3%28x%2B1%29\"$ 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( " $\"%282x%2B3%29%28x%2B1%29\"$ Combine like terms. Or factor out the common term $\"x%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2%2B5x%2B3\"$ factors to $\"%282x%2B3%29%28x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2x%5E2%2B5x%2B3=%282x%2B3%29%28x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%282x%2B3%29%28x%2B1%29\"$ to get $\"2x%5E2%2B5x%2B3\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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