Find all integers $x$ such that $|4x^2 - 12x - 27|$ is prime.
I first factored $|4x^2 - 12x - 27|$ as $(2x+3)(2x-9),$ but I was unsure where to go from there.
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3Well, how could that product be prime? – lulu Jan 15 '21 at 18:27
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2$x = - 1$ is an example. You see why? – Math Lover Jan 15 '21 at 18:31
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I'm not quite sure how I should do this beyond bashing it all. Could you elaborate? – questionasker Jan 15 '21 at 18:47
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OK see if my answer helps. – Math Lover Jan 15 '21 at 18:49
1 Answers
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Hint:
$|4x^2 - 12x - 27| = |(2x+3) \ (2x-9)|$
For it to be a prime number, one of the factors has to be $\pm1$ and absolute value of the other factor has to be the prime number.
So find $x$ when,
$2x+3 = \pm1$ or $2x - 9 = \pm1$ and check the value of the other factor.
There are only $4$ possible values of $x$ to check.
Math Lover
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