document.write( "Question 125882: Factor:\r
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\n" ); document.write( "\n" ); document.write( "x^2+3x-18 \n" ); document.write( "

Algebra.Com's Answer #92260 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"1x%5E2%2B3x-18\"$ we can see that the first term is $\"1x%5E2\"$ and the last term is $\"-18\"$ where the coefficients are 1 and -18 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -18 to get -18. Now what two numbers multiply to -18 and add to the middle coefficient 3? Let's list all of the factors of -18:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -18:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-9,-18 ...List the negative factors as well. 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)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(18)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(9)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(6)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 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 this list we can see that -3 and 6 add up to 3 and multiply to -18\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1x%5E2%2B3x-18\"$ , replace $\"3x\"$ with $\"-3x%2B6x\"$ (notice $\"-3x%2B6x\"$ adds up to $\"3x\"$ . So it is equivalent to $\"3x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%5E2%2Bhighlight%28-3x%2B6x%29%2B-18\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1x%5E2-3x%2B6x-18\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281x%5E2-3x%29%2B%286x-18%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-3%29%2B6%28x-3%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"6\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B6%29%28x-3%29\"$ Since we have a common term of $\"x-3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1x%5E2-3x%2B6x-18\"$ factors to $\"%28x%2B6%29%28x-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1x%5E2%2B3x-18\"$ factors to $\"%28x%2B6%29%28x-3%29\"$ (since $\"1x%5E2%2B3x-18\"$ is equivalent to $\"1x%5E2-3x%2B6x-18\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B3x-18\"$ factors to $\"%28x%2B6%29%28x-3%29\"$
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