document.write( "Question 502978: factor 9x^2-11x-58 \n" ); document.write( "

Algebra.Com's Answer #339031 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"9x%5E2-11x-58\"$ , we can see that the first coefficient is $\"9\"$ , the second coefficient is $\"-11\"$ , and the last term is $\"-58\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"9\"$ by the last term $\"-58\"$ to get $\"%289%29%28-58%29=-522\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-522\"$ (the previous product) and add to the second coefficient $\"-11\"$ ?\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 $\"-522\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-522\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6,9,18,29,58,87,174,261,522\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-9,-18,-29,-58,-87,-174,-261,-522\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 $\"-522\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-522) = -522
\n" ); document.write( "2*(-261) = -522
\n" ); document.write( "3*(-174) = -522
\n" ); document.write( "6*(-87) = -522
\n" ); document.write( "9*(-58) = -522
\n" ); document.write( "18*(-29) = -522
\n" ); document.write( "(-1)*(522) = -522
\n" ); document.write( "(-2)*(261) = -522
\n" ); document.write( "(-3)*(174) = -522
\n" ); document.write( "(-6)*(87) = -522
\n" ); document.write( "(-9)*(58) = -522
\n" ); document.write( "(-18)*(29) = -522\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 $\"-11\"$ :\r
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First Number	Second Number	Sum
1	-522	1+(-522)=-521
2	-261	2+(-261)=-259
3	-174	3+(-174)=-171
6	-87	6+(-87)=-81
9	-58	9+(-58)=-49
18	-29	18+(-29)=-11
-1	522	-1+522=521
-2	261	-2+261=259
-3	174	-3+174=171
-6	87	-6+87=81
-9	58	-9+58=49
-18	29	-18+29=11

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"18\"$ and $\"-29\"$ add to $\"-11\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"18\"$ and $\"-29\"$ both multiply to $\"-522\"$ and add to $\"-11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-11x\"$ with $\"18x-29x\"$ . Remember, $\"18\"$ and $\"-29\"$ add to $\"-11\"$ . So this shows us that $\"18x-29x=-11x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%5E2%2Bhighlight%2818x-29x%29-58\"$ Replace the second term $\"-11x\"$ with $\"18x-29x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%289x%5E2%2B18x%29%2B%28-29x-58%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%28x%2B2%29%2B%28-29x-58%29\"$ Factor out the GCF $\"9x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%28x%2B2%29-29%28x%2B2%29\"$ Factor out $\"29\"$ 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( " $\"%289x-29%29%28x%2B2%29\"$ Combine like terms. Or factor out the common term $\"x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"9x%5E2-11x-58\"$ factors to $\"%289x-29%29%28x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"9x%5E2-11x-58=%289x-29%29%28x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%289x-29%29%28x%2B2%29\"$ to get $\"9x%5E2-11x-58\"$ or by graphing the original expression and the answer (the two graphs should be identical). \n" ); document.write( "

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