document.write( "Question 195725: factor complety
\n" ); document.write( "5a*2-26a+5 \n" ); document.write( "

Algebra.Com's Answer #146764 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: use ^ for exponent instead of *\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"5a%5E2-26a%2B5\"$ , we can see that the first coefficient is $\"5\"$ , the second coefficient is $\"-26\"$ , and the last term is $\"5\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"5\"$ by the last term $\"5\"$ to get $\"%285%29%285%29=25\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"25\"$ (the previous product) and add to the second coefficient $\"-26\"$ ?\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 $\"25\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"25\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-5,-25\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 $\"25\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*25
\n" ); document.write( "5*5
\n" ); document.write( "(-1)*(-25)
\n" ); document.write( "(-5)*(-5)\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 $\"-26\"$ :\r
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First Number	Second Number	Sum
1	25	1+25=26
5	5	5+5=10
-1	-25	-1+(-25)=-26
-5	-5	-5+(-5)=-10

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-1\"$ and $\"-25\"$ add to $\"-26\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-1\"$ and $\"-25\"$ both multiply to $\"25\"$ and add to $\"-26\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-26a\"$ with $\"-a-25a\"$ . Remember, $\"-1\"$ and $\"-25\"$ add to $\"-26\"$ . So this shows us that $\"-a-25a=-26a\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5a%5E2%2Bhighlight%28-a-25a%29%2B5\"$ Replace the second term $\"-26a\"$ with $\"-a-25a\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%285a%5E2-a%29%2B%28-25a%2B5%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"a%285a-1%29%2B%28-25a%2B5%29\"$ Factor out the GCF $\"a\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"a%285a-1%29-5%285a-1%29\"$ Factor out $\"5\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28a-5%29%285a-1%29\"$ Combine like terms. Or factor out the common term $\"5a-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"5a%5E2-26a%2B5\"$ factors to $\"%28a-5%29%285a-1%29\"$ .\r
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