document.write( "Question 125884: Factor:\r
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\n" ); document.write( "\n" ); document.write( "x^2+6x-16\r
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Algebra.Com's Answer #92258 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"1x%5E2%2B6x-16\"$ we can see that the first term is $\"1x%5E2\"$ and the last term is $\"-16\"$ where the coefficients are 1 and -16 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -16 to get -16. Now what two numbers multiply to -16 and add to the middle coefficient 6? Let's list all of the factors of -16:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -16:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-8 ...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 -16\r
\n" ); document.write( "\n" ); document.write( "(1)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-8)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(16)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(8)\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 6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 6\r
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First Number	Second Number	Sum
1	-16	1+(-16)=-15
2	-8	2+(-8)=-6
-1	16	-1+16=15
-2	8	-2+8=6

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -2 and 8 add up to 6 and multiply to -16\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1x%5E2%2B6x-16\"$ , replace $\"6x\"$ with $\"-2x%2B8x\"$ (notice $\"-2x%2B8x\"$ adds up to $\"6x\"$ . So it is equivalent to $\"6x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%5E2%2Bhighlight%28-2x%2B8x%29%2B-16\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1x%5E2-2x%2B8x-16\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281x%5E2-2x%29%2B%288x-16%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29%2B8%28x-2%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"8\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-2%29\"$ Since we have a common term of $\"x-2\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1x%5E2-2x%2B8x-16\"$ factors to $\"%28x%2B8%29%28x-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1x%5E2%2B6x-16\"$ factors to $\"%28x%2B8%29%28x-2%29\"$ (since $\"1x%5E2%2B6x-16\"$ is equivalent to $\"1x%5E2-2x%2B8x-16\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B6x-16\"$ factors to $\"%28x%2B8%29%28x-2%29\"$
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