document.write( "Question 179600: Factor w^2-3w-18= \n" ); document.write( "

Algebra.Com's Answer #134517 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"w%5E2-3w-18\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-3\"$ , and the last term is $\"-18\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-18\"$ to get $\"%281%29%28-18%29=-18\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-18\"$ (the previous product) and add to the second coefficient $\"-3\"$ ?\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 $\"-18\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-18\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6,9,18\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-9,-18\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 $\"-18\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-18)
\n" ); document.write( "2*(-9)
\n" ); document.write( "3*(-6)
\n" ); document.write( "(-1)*(18)
\n" ); document.write( "(-2)*(9)
\n" ); document.write( "(-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 $\"-3\"$ :\r
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First Number	Second Number	Sum
1	-18	1+(-18)=-17
2	-9	2+(-9)=-7
3	-6	3+(-6)=-3
-1	18	-1+18=17
-2	9	-2+9=7
-3	6	-3+6=3

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"3\"$ and $\"-6\"$ add to $\"-3\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"3\"$ and $\"-6\"$ both multiply to $\"-18\"$ and add to $\"-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-3w\"$ with $\"3w-6w\"$ . Remember, $\"3\"$ and $\"-6\"$ add to $\"-3\"$ . So this shows us that $\"3w-6w=-3w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"w%5E2%2Bhighlight%283w-6w%29-18\"$ Replace the second term $\"-3w\"$ with $\"3w-6w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28w%5E2%2B3w%29%2B%28-6w-18%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"w%28w%2B3%29%2B%28-6w-18%29\"$ Factor out the GCF $\"w\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"w%28w%2B3%29-6%28w%2B3%29\"$ Factor out $\"6\"$ 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( " $\"%28w-6%29%28w%2B3%29\"$ Combine like terms. Or factor out the common term $\"w%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"w%5E2-3w-18\"$ factors to $\"%28w-6%29%28w%2B3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%28w-6%29%28w%2B3%29\"$ to get $\"w%5E2-3w-18\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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