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Given x^5 + x^2 + 1 is irreducible over F2, let F32 = F2[X]/(X^5 + X^2...

Given x^5 + x^2 + 1 is irreducible over F2, let F32 = F2[X]/(X^5 + X^2 + 1) with f = [X].
Please represent any element g where

g = a4*f^4 + a3*f^3 + a2*f^2 + a1*f + a0

1. If g1 = f^4 + f^2 and g2 = f^2 + f + 1, compute g1*g2
2. Compute f^11
3. Is the polynomial x5 + x2 + 1 primitive? Please explain your answer

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