document.write( "Question 112001: Here's another I can't factor:\r
\n" ); document.write( "\n" ); document.write( "(-8k^2 + 6K + 9)\r
\n" ); document.write( "\n" ); document.write( "thanks very much,
\n" ); document.write( "CJ \n" ); document.write( "

Algebra.Com's Answer #81691 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at $\"-8k%5E2%2B6k%2B9\"$ we can see that the first term is $\"-8k%5E2\"$ and the last term is $\"9\"$ where the coefficients are -8 and 9 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient -8 and the last coefficient 9 to get -72. Now what two numbers multiply to -72 and add to 6? Let's list all of the factors of -72:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -72:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,9,12,18,24,36,72\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72 ...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 -72\r
\n" ); document.write( "\n" ); document.write( "(1)*(-72)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-36)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-18)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(8)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(72)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(36)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(24)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(18)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(9)\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	-72	1+(-72)=-71
2	-36	2+(-36)=-34
3	-24	3+(-24)=-21
4	-18	4+(-18)=-14
6	-12	6+(-12)=-6
8	-9	8+(-9)=-1
-1	72	-1+72=71
-2	36	-2+36=34
-3	24	-3+24=21
-4	18	-4+18=14
-6	12	-6+12=6
-8	9	-8+9=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -6 and 12 add up to 6 and multiply to -72\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"-8k%5E2%2B6k%2B9\"$ , replace $\"6k\"$ with $\"-6k%2B12k\"$ (notice $\"-6k%2B12k\"$ adds up to $\"6k\"$ . So it is equivalent to $\"6k\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"-8k%5E2%2Bhighlight%28-6k%2B12k%29%2B9\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"-8k%5E2-6k%2B12k%2B9\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-8k%5E2-6k%29%2B%2812k%2B9%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"-2k%284k%2B3%29%2B3%284k%2B3%29\"$ Factor out the GCF of $\"-2k\"$ out of the first group. Factor out the GCF of $\"3\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-2k%2B3%29%284k%2B3%29\"$ Since we have a common term of $\"4k%2B3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"-8k%5E2-6k%2B12k%2B9\"$ factors to $\"%28-2k%2B3%29%284k%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"-8k%5E2%2B6k%2B9\"$ factors to $\"%28-2k%2B3%29%284k%2B3%29\"$ (since $\"-8k%5E2%2B6k%2B9\"$ is equivalent to $\"-8k%5E2-6k%2B12k%2B9\"$ )
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