Question 332239: factor 2x^2 -240x+5500
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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Looking at the expression , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,5,10,11,22,25,50,55,110,125,250,275,550,1375,2750
-1,-2,-5,-10,-11,-22,-25,-50,-55,-110,-125,-250,-275,-550,-1375,-2750
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*2750 = 2750
2*1375 = 2750
5*550 = 2750
10*275 = 2750
11*250 = 2750
22*125 = 2750
25*110 = 2750
50*55 = 2750
(-1)*(-2750) = 2750
(-2)*(-1375) = 2750
(-5)*(-550) = 2750
(-10)*(-275) = 2750
(-11)*(-250) = 2750
(-22)*(-125) = 2750
(-25)*(-110) = 2750
(-50)*(-55) = 2750
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| 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 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So simply factors to
In other words,  .
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