integer x for which f(x) is prime

Since by Fermat's Little Theorem x^3 \equiv x \pmod{3} we have

x^3 +6x^2+2x-6 \equiv 6x^2+3x-6 \equiv 0 \pmod{3}

Hence we only need to solve the cubics x^3 +6x^2+2x-6 = \pm 3 for integer solutions

which have their only integer roots as -1 and 1 respectively

Thanks Pritish., Next time I will not post Such Type of Questions.

@piritish , when u know that this is not for jee (and this is true) why do u waste ur time over here? In stead of coercing others to stop their discussion why can't u simply ignore this type of threads ?

in a way jagdish cannot be faulted. If the polynomial could have been factorised, then the question would have fallen in jee syllabus! He couldnt have known beforehand that the solution would use FLT.

remember having seen it earlier http://www.goiit.com/posts/list/algebra-prime-no-1101041.htm