document.write( "Question 117342: Please, having some problems with this one\r
\n" ); document.write( "\n" ); document.write( "x^3- 26x^2 +48x\r
\n" ); document.write( "\n" ); document.write( "Thank you ahaead of time.\r
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Algebra.Com's Answer #85369 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"x%5E3-26x%5E2%2B48x\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%5E2-26x%2B48%29\"$ Factor out the GCF $\"x\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"x%5E2-26x%2B48\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"x%5E2-26x%2B48\"$ we can see that the first term is $\"x%5E2\"$ and the last term is $\"48\"$ where the coefficients are 1 and 48 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 48 to get 48. Now what two numbers multiply to 48 and add to the middle coefficient -26? Let's list all of the factors of 48:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 48:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,48\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...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 48\r
\n" ); document.write( "\n" ); document.write( "1*48\r
\n" ); document.write( "\n" ); document.write( "2*24\r
\n" ); document.write( "\n" ); document.write( "3*16\r
\n" ); document.write( "\n" ); document.write( "4*12\r
\n" ); document.write( "\n" ); document.write( "6*8\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-48)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-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 -26? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -26\r
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First Number	Second Number	Sum
1	48	1+48=49
2	24	2+24=26
3	16	3+16=19
4	12	4+12=16
6	8	6+8=14
-1	-48	-1+(-48)=-49
-2	-24	-2+(-24)=-26
-3	-16	-3+(-16)=-19
-4	-12	-4+(-12)=-16
-6	-8	-6+(-8)=-14

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -2 and -24 add up to -26 and multiply to 48\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"x%5E2-26x%2B48\"$ , replace $\"-26x\"$ with $\"-2x%2B-24x\"$ (notice $\"-2x%2B-24x\"$ adds up to $\"-26x\"$ . So it is equivalent to $\"-26x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28-2x%2B-24x%29%2B48\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"x%5E2-2x-24x%2B48\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-2x%29%2B%28-24x%2B48%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29-24%28x-2%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-24\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-24%29%28x-2%29\"$ Since we have a common term of $\"x-2\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-26x%2B48\"$ factors to $\"%28x-24%29%28x-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-24%29%28x-2%29\"$ Reintroduce the GCF\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E3-26x%5E2%2B48x\"$ factors to $\"x%28x-24%29%28x-2%29\"$
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