document.write( "Question 168402: i need help with this factoring problem $\"+7y%5E2%2B7y-18+\"$
\n" ); document.write( " and also this one with the negative first kinda threw me off.
\n" ); document.write( " $\"-5ab%5E2%2B10a%5E2b-15ab+\"$ \n" ); document.write( "

Algebra.Com's Answer #124152 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"7y%5E2%2B7y-18\"$ , we can see that the first coefficient is $\"7\"$ , the second coefficient is $\"7\"$ , and the last term is $\"-18\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"7\"$ by the last term $\"-18\"$ to get $\"%287%29%28-18%29=-126\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-126\"$ (the previous product) and add to the second coefficient $\"7\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-126\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-126\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6,7,9,14,18,21,42,63,126\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-7,-9,-14,-18,-21,-42,-63,-126\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. 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 $\"-126\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-126)
\n" ); document.write( "2*(-63)
\n" ); document.write( "3*(-42)
\n" ); document.write( "6*(-21)
\n" ); document.write( "7*(-18)
\n" ); document.write( "9*(-14)
\n" ); document.write( "(-1)*(126)
\n" ); document.write( "(-2)*(63)
\n" ); document.write( "(-3)*(42)
\n" ); document.write( "(-6)*(21)
\n" ); document.write( "(-7)*(18)
\n" ); document.write( "(-9)*(14)\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"7\"$ :\r
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First Number	Second Number	Sum
1	-126	1+(-126)=-125
2	-63	2+(-63)=-61
3	-42	3+(-42)=-39
6	-21	6+(-21)=-15
7	-18	7+(-18)=-11
9	-14	9+(-14)=-5
-1	126	-1+126=125
-2	63	-2+63=61
-3	42	-3+42=39
-6	21	-6+21=15
-7	18	-7+18=11
-9	14	-9+14=5

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that there are NO pairs of numbers which add to $\"7\"$ . \r
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\n" ); document.write( "\n" ); document.write( "So $\"7y%5E2%2B7y-18\"$ CANNOT be factored.\r
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\n" ); document.write( "\n" ); document.write( " $\"-5ab%5E2%2B10a%5E2b-15ab\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"-5ab%28b-2a%2B3%29\"$ Factor out the GCF $\"-5ab\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since the inner term contains no other common terms or exponents, this is as far as we go.\r
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\n" ); document.write( "\n" ); document.write( "So $\"-5ab%5E2%2B10a%5E2b-15ab\"$ factors to $\"-5ab%28b-2a%2B3%29\"$ \n" ); document.write( "

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