document.write( "Question 193101: 40x^2-48x-88 \n" ); document.write( "

Algebra.Com's Answer #144946 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"40x%5E2-48x-88\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"8%285x%5E2-6x-11%29\"$ Factor out the GCF $\"8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"5x%5E2-6x-11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"5x%5E2-6x-11\"$ we can see that the first term is $\"5x%5E2\"$ and the last term is $\"-11\"$ where the coefficients are 5 and -11 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 5 and the last coefficient -11 to get -55. Now what two numbers multiply to -55 and add to the middle coefficient -6? Let's list all of the factors of -55:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -55:\r
\n" ); document.write( "\n" ); document.write( "1,5,11,55\r
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\n" ); document.write( "\n" ); document.write( "-1,-5,-11,-55 ...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 -55\r
\n" ); document.write( "\n" ); document.write( "(1)*(-55)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-11)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(55)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(11)\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	-55	1+(-55)=-54
5	-11	5+(-11)=-6
-1	55	-1+55=54
-5	11	-5+11=6

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 5 and -11 add up to -6 and multiply to -55\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"5x%5E2-6x-11\"$ , replace $\"-6x\"$ with $\"5x%2B-11x\"$ (notice $\"5x%2B-11x\"$ adds up to $\"-6x\"$ . So it is equivalent to $\"-6x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%5E2%2Bhighlight%285x%2B-11x%29%2B-11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"5x%5E2%2B5x-11x-11\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%285x%5E2%2B5x%29%2B%28-11x-11%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%28x%2B1%29-11%28x%2B1%29\"$ Factor out the GCF of $\"5x\"$ out of the first group. Factor out the GCF of $\"-11\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%285x-11%29%28x%2B1%29\"$ Since we have a common term of $\"x%2B1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"5x%5E2%2B5x-11x-11\"$ factors to $\"%285x-11%29%28x%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"5x%5E2-6x-11\"$ factors to $\"%285x-11%29%28x%2B1%29\"$ (since $\"5x%5E2-6x-11\"$ is equivalent to $\"5x%5E2%2B5x-11x-11\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"8%285x%5E2-6x-11%29\"$ and factors further to $\"8%285x-11%29%28x%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"40x%5E2-48x-88\"$ completely factors to $\"8%285x-11%29%28x%2B1%29\"$ \r
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