Question

Factor x^2 -3x-3 in F5(x) p=5

Answer 1

$-3=2-5\implies -3\mod5=2\mod5$

When taking a polynomial modulo $n$, you reduce its terms' coefficients modulo $n$, so that, in conjunction with the result above,

$x^2-3x-3\equiv x^2-3x+2\mod5$

For completeness, the linear term's coefficient should also get reduced in the same way as the constant term, so that

$x^2-3x-3\equiv x^2+2x+2\mod5$