SOLUTION: factor 2x^2 -240x+5500

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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