document.write( "Question 146889This question is from textbook
\n" ); document.write( ": 35x^2 - 2x - 1 \n" ); document.write( "

Algebra.Com's Answer #107274 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that you want to factor.\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"35x%5E2-2x-1\"$ we can see that the first term is $\"35x%5E2\"$ and the last term is $\"-1\"$ where the coefficients are 35 and -1 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 35 and the last coefficient -1 to get -35. Now what two numbers multiply to -35 and add to the middle coefficient -2? Let's list all of the factors of -35:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -35:\r
\n" ); document.write( "\n" ); document.write( "1,5,7,35\r
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\n" ); document.write( "\n" ); document.write( "-1,-5,-7,-35 ...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 -35\r
\n" ); document.write( "\n" ); document.write( "(1)*(-35)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-7)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(35)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(7)\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 -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2\r
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First Number	Second Number	Sum
1	-35	1+(-35)=-34
5	-7	5+(-7)=-2
-1	35	-1+35=34
-5	7	-5+7=2

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 5 and -7 add up to -2 and multiply to -35\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"35x%5E2-2x-1\"$ , replace $\"-2x\"$ with $\"5x%2B-7x\"$ (notice $\"5x%2B-7x\"$ adds up to $\"-2x\"$ . So it is equivalent to $\"-2x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"35x%5E2%2Bhighlight%285x%2B-7x%29%2B-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"35x%5E2%2B5x-7x-1\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2835x%5E2%2B5x%29%2B%28-7x-1%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%287x%2B1%29-1%287x%2B1%29\"$ Factor out the GCF of $\"5x\"$ out of the first group. Factor out the GCF of $\"-1\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%285x-1%29%287x%2B1%29\"$ Since we have a common term of $\"7x%2B1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"35x%5E2%2B5x-7x-1\"$ factors to $\"%285x-1%29%287x%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"35x%5E2-2x-1\"$ factors to $\"%285x-1%29%287x%2B1%29\"$ (since $\"35x%5E2-2x-1\"$ is equivalent to $\"35x%5E2%2B5x-7x-1\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"35x%5E2-2x-1\"$ factors to $\"%285x-1%29%287x%2B1%29\"$
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