Investigate if the following polynomial in Q [x] is reducible or irreducible: $x^3+6x^2+8x+4$
Dear Community, it took me some hours to think about it and i cant come to a good solution, i would be so happy if someone can show me how to do this right...^^
So this is my attempt:
$p(x) = x^3+6x^2+8x+4$
substitute with $(x-1)$ gives:
$p'(x-1) = x^3+3x^2-x+1$
modulo $2$ gives:
$p'(x-1) = x^3+x^2+x+1$
now substitute with $(x+1)$
$p''(x+1) = x^3+4x^2+6x+4$
now we se $x=-2$ we get $(x+2)(x^2+2x+2)$ so its reducible?