SOLUTION: Factor completely 2x^2 – 20x -50

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Question 617823: Factor completely 2x^2 – 20x -50

Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
2*(x^2-10x-25)
find factors of -50 which add up to -10
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


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 :

1,5,25

-1,-5,-25



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



These factors pair up and multiply to .

1*(-25) = -25
5*(-5) = -25
(-1)*(25) = -25
(-5)*(5) = -25


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1-251+(-25)=-24
5-55+(-5)=0
-125-1+25=24
-55-5+5=0




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



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





Answer:



So doesn't factor at all (over the rational numbers).



So is prime.
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