SOLUTION: If A and B are positive integers such that both 4x2 +Ax+36 and 6x2+Bx+24 factor over the integers, find the largest possible value of A-B.

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Question 793182: If A and B are positive integers such that both 4x2 +Ax+36 and 6x2+Bx+24 factor over the integers, find the largest possible value of A-B.
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
If can be factored, to find the factors I would start by looking for pairs of factors of
With , A would be the sum of one of those factor pairs.
Here are the factor pairs and their sums:








If can be factored, to find the factors I would start by looking for pairs of factors of
With , B would be the sum of one of those factor pairs, which were already listed above.

To get the largest possible value of A-B, I need to pair possible value of A with the smallest possible value of B.
So the largest difference would be

In that case the factorings would be
and

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