document.write( "Question 481981: Okay so I am having a brain-freeze on how to factor more challenging polynomials, how do you factor:
\n" ); document.write( "40k^2-112k+24 \n" ); document.write( "

Algebra.Com's Answer #330005 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"40k%5E2-112k%2B24\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"8%285k%5E2-14k%2B3%29\"$ Factor out the GCF $\"8\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"5k%5E2-14k%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"5k%5E2-14k%2B3\"$ , we can see that the first coefficient is $\"5\"$ , the second coefficient is $\"-14\"$ , and the last term is $\"3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"5\"$ by the last term $\"3\"$ to get $\"%285%29%283%29=15\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"15\"$ (the previous product) and add to the second coefficient $\"-14\"$ ?\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 $\"15\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"15\"$ :\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 $\"15\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*15 = 15
\n" ); document.write( "3*5 = 15
\n" ); document.write( "(-1)*(-15) = 15
\n" ); document.write( "(-3)*(-5) = 15\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 $\"-14\"$ :\r
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First Number	Second Number	Sum
1	15	1+15=16
3	5	3+5=8
-1	-15	-1+(-15)=-16
-3	-5	-3+(-5)=-8

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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 $\"-14\"$ . So $\"5k%5E2-14k%2B3\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"40k%5E2-112k%2B24\"$ simply factors to $\"8%285k%5E2-14k%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"40k%5E2-112k%2B24=8%285k%5E2-14k%2B3%29\"$ .
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