What is the greatest integer $x$ such that $|6x^2-47x+15-28x|$ is prime?
I think you use factorization here, but I don't know how.
I don't believe that an integer exists to make this prime
Simplifying we have
l 6x^2 - 75x + 15 l
l 3 ( 2x^2 - 25x + 5) l
3 l 2x^2 -25x + 5 l
The only way this can be prime is if the expression in the absolute value bars is either = 1 or = -1
2x^2 - 25x + 5 = 1
2x^2 - 25x + 4 = 0
Using the Q formula x is not an integer because the discrminant = 25^2 - 4(2)*(4) = 593 which is not a perfect square
2x^2 - 25x + 5 = -1
2x^2 - 25x + 6 = 0
The discriminant = 25^2 - 4* 2 * 5 = 585 which is also not a perfect square