SOLUTION: 6x^2+18x-600 Factor, if possible. Be sure to factor completely. Always factor out the greatest commone factor first, if one exist. thanks.

Question 725322: 6x^2+18x-600
Factor, if possible. Be sure to factor completely. Always factor out the greatest commone factor first, if one exist.
thanks.

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 :
1,2,4,5,10,20,25,50,100
-1,-2,-4,-5,-10,-20,-25,-50,-100

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-100) = -100
2*(-50) = -100
4*(-25) = -100
5*(-20) = -100
10*(-10) = -100
(-1)*(100) = -100
(-2)*(50) = -100
(-4)*(25) = -100
(-5)*(20) = -100
(-10)*(10) = -100

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	-100	1+(-100)=-99
2	-50	2+(-50)=-48
4	-25	4+(-25)=-21
5	-20	5+(-20)=-15
10	-10	10+(-10)=0
-1	100	-1+100=99
-2	50	-2+50=48
-4	25	-4+25=21
-5	20	-5+20=15
-10	10	-10+10=0

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So simply factors to

In other words, .

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