1. The problem statement, all variables and given/known data If p(x) ∈F[x] is of degree 3, and p(x)=a0+a1∗x+a2∗x2+a3∗x3, show that p(x) is irreducible over F if there is no element r∈F such that a0+a1∗r+a2∗r2+a3∗r3 =0. 2. Relevant equations 3. The attempt at a solution Is this approach correct? If p(x) is reducible, then there exists ax + b such that a, b ε F and a≠0. And p(x) = (ax + b)(cx^2 + dx + e). Then an r exists such that p(r) = 0. Thank you.