document.write( "Question 129934: 9usquared-9u+2 \n" ); document.write( "

Algebra.Com's Answer #94885 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to factor?\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"9u%5E2-9u%2B2\"$ we can see that the first term is $\"9u%5E2\"$ and the last term is $\"2\"$ where the coefficients are 9 and 2 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 9 and the last coefficient 2 to get 18. Now what two numbers multiply to 18 and add to the middle coefficient -9? Let's list all of the factors of 18:\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
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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 two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9\r
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First Number	Second Number	Sum
1	18	1+18=19
2	9	2+9=11
3	6	3+6=9
-1	-18	-1+(-18)=-19
-2	-9	-2+(-9)=-11
-3	-6	-3+(-6)=-9

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -3 and -6 add up to -9 and multiply to 18\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"9u%5E2-9u%2B2\"$ , replace $\"-9u\"$ with $\"-3u%2B-6u\"$ (notice $\"-3u%2B-6u\"$ adds up to $\"-9u\"$ . So it is equivalent to $\"-9u\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"9u%5E2%2Bhighlight%28-3u%2B-6u%29%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"9u%5E2-3u-6u%2B2\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%289u%5E2-3u%29%2B%28-6u%2B2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"3u%283u-1%29-2%283u-1%29\"$ Factor out the GCF of $\"3u\"$ out of the first group. Factor out the GCF of $\"-2\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%283u-2%29%283u-1%29\"$ Since we have a common term of $\"3u-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"9u%5E2-3u-6u%2B2\"$ factors to $\"%283u-2%29%283u-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"9u%5E2-9u%2B2\"$ factors to $\"%283u-2%29%283u-1%29\"$ (since $\"9u%5E2-9u%2B2\"$ is equivalent to $\"9u%5E2-3u-6u%2B2\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"9u%5E2-9u%2B2\"$ factors to $\"%283u-2%29%283u-1%29\"$
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