document.write( "Question 368669: 5c^2-17c+14 \n" ); document.write( "

Algebra.Com's Answer #262688 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that you want to factor this right? Please post the full instructions.\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"5c%5E2-17c%2B14\"$ we can see that the first term is $\"5c%5E2\"$ and the last term is $\"14\"$ where the coefficients are 5 and 14 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 5 and the last coefficient 14 to get 70. Now what two numbers multiply to 70 and add to the middle coefficient -17? Let's list all of the factors of 70:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 70:\r
\n" ); document.write( "\n" ); document.write( "1,2,5,7,10,14,35,70\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-5,-7,-10,-14,-35,-70 ...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 70\r
\n" ); document.write( "\n" ); document.write( "1*70\r
\n" ); document.write( "\n" ); document.write( "2*35\r
\n" ); document.write( "\n" ); document.write( "5*14\r
\n" ); document.write( "\n" ); document.write( "7*10\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-70)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-35)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-14)\r
\n" ); document.write( "\n" ); document.write( "(-7)*(-10)\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 -17? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -17\r
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First Number	Second Number	Sum
1	70	1+70=71
2	35	2+35=37
5	14	5+14=19
7	10	7+10=17
-1	-70	-1+(-70)=-71
-2	-35	-2+(-35)=-37
-5	-14	-5+(-14)=-19
-7	-10	-7+(-10)=-17

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -7 and -10 add up to -17 and multiply to 70\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"5c%5E2-17c%2B14\"$ , replace $\"-17c\"$ with $\"-7c%2B-10c\"$ (notice $\"-7c%2B-10c\"$ adds up to $\"-17c\"$ . So it is equivalent to $\"-17c\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"5c%5E2%2Bhighlight%28-7c%2B-10c%29%2B14\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"5c%5E2-7c-10c%2B14\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%285c%5E2-7c%29%2B%28-10c%2B14%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"c%285c-7%29-2%285c-7%29\"$ Factor out the GCF of $\"c\"$ 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( " $\"%28c-2%29%285c-7%29\"$ Since we have a common term of $\"5c-7\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"5c%5E2-7c-10c%2B14\"$ factors to $\"%28c-2%29%285c-7%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"5c%5E2-17c%2B14\"$ factors to $\"%28c-2%29%285c-7%29\"$ (since $\"5c%5E2-17c%2B14\"$ is equivalent to $\"5c%5E2-7c-10c%2B14\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"5c%5E2-17c%2B14\"$ factors to $\"%28c-2%29%285c-7%29\"$
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