perplexus.info :: Just Math : Factorizable Expressions

Factorizable Expressions (Posted on 2015-10-21)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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re: The whole story? More.

| Comment 2 of 4 |

(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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