Thread: Find roots of poly in Z_5[x]

Find roots and factor 3x^4 + x^2 + 1 in Z_5[x]

Roots:
f(0) = 1
f(1) = 0 in Z5
f(2) = 3 in Z5
f(3) = 3 in Z5
f(4) = 0 in Z5

So Ive only found 2 roots: 1 and 4. How do I find the other two?

divide by (x - 1)(x - 4).

Yeah I figured it out. What I was hung up on was the fact that while working in Z5 and with a poly of degree 4, it doesn't necessarily imply that there are 4 roots. But thanks for the reply.