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.
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Answer:
So simply factors to
In other words,  .
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