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Factorizable Expressions (Posted on 2015-10-21) Difficulty: 2 of 5
Each of A and B is a positive integer.

Find the relationship between A and B such that each of the expressions:
x2 + A*x + B and x2 + A*x + B + 2 is resolvable into factors of the form (x+p)(x+q), for positive integers p and q.

No Solution Yet Submitted by K Sengupta    
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Solution re: The whole story? More. | Comment 2 of 3 |
(In reply to The whole story? by Jer)

I realized I didn't actually show my solution b=(a^2 - 9)/4 works.

The first quadratic can be rewritten and factored as
x2 + A*x + (A2 - 9)/4 = (x + (A+3)/2)(x + (A-3)/2)
and the second as
x2 + A*x + (A2 - 1)/4 = (x + (A+1)/2)(x + (A-1)/2)

[Again, since A is odd, those fractions will yield positive integers for p and q.]

  Posted by Jer on 2015-10-22 07:21:33
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