Let $x^{14} - 16$ be an element of the polynomial ring $E =\mathbb{Z}[x]$ and let the bar notation to denote passage to the quotient ring $\mathbb{Z}[x]/(x^4 - 16)$.
a) Find a polynomial of degree less than or equal to 3 that is congruent to $7x^{13} -11x^9+5x^5 -2x^3+3 \pmod {x^4-16}$.
b) Prove that $\overline{x-2}$ and $\overline{x+2}$ are zero divisors in $\overline{E}$.
I tried it out, but not sure about notation and such. Can you please run through the problem solution? Thank you.