In order to find a root of a(x) in a finite field F, the simplest method (if F is small) is to test every element of F by substitution into the equation a(x) = 0. 1 Find all the roots of the following polynomials in z 5[x], and factor the polynomials: x+x+x+1; 3x4+x+1; x+1; 4+1; 4+4