document.write( "Question 332239: factor 2x^2 -240x+5500 \n" ); document.write( "

Algebra.Com's Answer #238103 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2-240x%2B5500\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"2%28x%5E2-120x%2B2750%29\"$ Factor out the GCF $\"2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"x%5E2-120x%2B2750\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-120x%2B2750\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-120\"$ , and the last term is $\"2750\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"2750\"$ to get $\"%281%29%282750%29=2750\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"2750\"$ (the previous product) and add to the second coefficient $\"-120\"$ ?\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 $\"2750\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"2750\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,5,10,11,22,25,50,55,110,125,250,275,550,1375,2750\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-5,-10,-11,-22,-25,-50,-55,-110,-125,-250,-275,-550,-1375,-2750\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 $\"2750\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*2750 = 2750
\n" ); document.write( "2*1375 = 2750
\n" ); document.write( "5*550 = 2750
\n" ); document.write( "10*275 = 2750
\n" ); document.write( "11*250 = 2750
\n" ); document.write( "22*125 = 2750
\n" ); document.write( "25*110 = 2750
\n" ); document.write( "50*55 = 2750
\n" ); document.write( "(-1)*(-2750) = 2750
\n" ); document.write( "(-2)*(-1375) = 2750
\n" ); document.write( "(-5)*(-550) = 2750
\n" ); document.write( "(-10)*(-275) = 2750
\n" ); document.write( "(-11)*(-250) = 2750
\n" ); document.write( "(-22)*(-125) = 2750
\n" ); document.write( "(-25)*(-110) = 2750
\n" ); document.write( "(-50)*(-55) = 2750\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 $\"-120\"$ :\r
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First Number	Second Number	Sum
1	2750	1+2750=2751
2	1375	2+1375=1377
5	550	5+550=555
10	275	10+275=285
11	250	11+250=261
22	125	22+125=147
25	110	25+110=135
50	55	50+55=105
-1	-2750	-1+(-2750)=-2751
-2	-1375	-2+(-1375)=-1377
-5	-550	-5+(-550)=-555
-10	-275	-10+(-275)=-285
-11	-250	-11+(-250)=-261
-22	-125	-22+(-125)=-147
-25	-110	-25+(-110)=-135
-50	-55	-50+(-55)=-105

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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 $\"-120\"$ . So $\"x%5E2-120x%2B2750\"$ 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 $\"2x%5E2-240x%2B5500\"$ simply factors to $\"2%28x%5E2-120x%2B2750%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2x%5E2-240x%2B5500=2%28x%5E2-120x%2B2750%29\"$ .
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