document.write( "Question 725822: factor\r
\n" ); document.write( "\n" ); document.write( "3x^2 + 8x - 3 \n" ); document.write( "

Algebra.Com's Answer #444325 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3x%5E2%2B8x-3\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"8\"$ , and the last term is $\"-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-3\"$ to get $\"%283%29%28-3%29=-9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-9\"$ (the previous product) and add to the second coefficient $\"8\"$ ?\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 $\"-9\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-9\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-9\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 $\"-9\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-9) = -9
\n" ); document.write( "3*(-3) = -9
\n" ); document.write( "(-1)*(9) = -9
\n" ); document.write( "(-3)*(3) = -9\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 $\"8\"$ :\r
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First Number	Second Number	Sum
1	-9	1+(-9)=-8
3	-3	3+(-3)=0
-1	9	-1+9=8
-3	3	-3+3=0

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-1\"$ and $\"9\"$ add to $\"8\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-1\"$ and $\"9\"$ both multiply to $\"-9\"$ and add to $\"8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"8x\"$ with $\"-x%2B9x\"$ . Remember, $\"-1\"$ and $\"9\"$ add to $\"8\"$ . So this shows us that $\"-x%2B9x=8x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2%2Bhighlight%28-x%2B9x%29-3\"$ Replace the second term $\"8x\"$ with $\"-x%2B9x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x%5E2-x%29%2B%289x-3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x-1%29%2B%289x-3%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x-1%29%2B3%283x-1%29\"$ 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( " $\"%28x%2B3%29%283x-1%29\"$ Combine like terms. Or factor out the common term $\"3x-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B8x-3\"$ factors to $\"%28x%2B3%29%283x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"3x%5E2%2B8x-3=%28x%2B3%29%283x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B3%29%283x-1%29\"$ to get $\"3x%5E2%2B8x-3\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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