We have:
$$p(x) = x^3+x+1\in\mathbb{Z}_5[x]$$
First of all, I tried to prove that there are no roots in $\mathbb{Z}_5$, so I tried all of them:
$$p(0) = 1\\p(1) = 3\\p(2) = 1\\p(3) = 1\\p(4) = 4$$ So since there are no roots, I can't reduce this polynomial to a linear polynomial times a 2nd degree one. T
