document.write( "Question 176141: Make sure to superscript all exponents. If you believe that a polynomial is not factorable, label it as prime, Show all stages of factoring separately(i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again).\r
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Algebra.Com's Answer #131254 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E3-26x%5E2%2B80x\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%28x%5E2-13x%2B40%29\"$ Factor out the GCF $\"2x\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"x%5E2-13x%2B40\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"1x%5E2-13x%2B40\"$ we can see that the first term is $\"1x%5E2\"$ and the last term is $\"40\"$ where the coefficients are 1 and 40 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 40 to get 40. Now what two numbers multiply to 40 and add to the middle coefficient -13? Let's list all of the factors of 40:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 40:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-8,-10,-20,-40 ...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 40\r
\n" ); document.write( "\n" ); document.write( "1*40\r
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\n" ); document.write( "\n" ); document.write( "4*10\r
\n" ); document.write( "\n" ); document.write( "5*8\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-40)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-8)\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 -13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -13\r
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First Number	Second Number	Sum
1	40	1+40=41
2	20	2+20=22
4	10	4+10=14
5	8	5+8=13
-1	-40	-1+(-40)=-41
-2	-20	-2+(-20)=-22
-4	-10	-4+(-10)=-14
-5	-8	-5+(-8)=-13

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -5 and -8 add up to -13 and multiply to 40\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1x%5E2-13x%2B40\"$ , replace $\"-13x\"$ with $\"-5x%2B-8x\"$ (notice $\"-5x%2B-8x\"$ adds up to $\"-13x\"$ . So it is equivalent to $\"-13x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%5E2%2Bhighlight%28-5x%2B-8x%29%2B40\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1x%5E2-5x-8x%2B40\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281x%5E2-5x%29%2B%28-8x%2B40%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-5%29-8%28x-5%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-8\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-8%29%28x-5%29\"$ Since we have a common term of $\"x-5\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1x%5E2-5x-8x%2B40\"$ factors to $\"%28x-8%29%28x-5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1x%5E2-13x%2B40\"$ factors to $\"%28x-8%29%28x-5%29\"$ (since $\"1x%5E2-13x%2B40\"$ is equivalent to $\"1x%5E2-5x-8x%2B40\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"2x%28x%5E2-13x%2B40%29\"$ and factors further to $\"2x%28x-8%29%28x-5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E3-26x%5E2%2B80x\"$ completely factors to $\"2x%28x-8%29%28x-5%29\"$ \r
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