Write $f(x) = x^{5} + 2x^{2} + 2x + 2$ as a product of irreducible polynomials over $\mathbb{Z}_{3}[x], \mathbb{Z}_{5}[x], \mathbb{Z}_{7}[x]$.
I tried using the Factor Theorem but I couldn't find any zeroes in the respective rings.
2026-03-28 17:05:43.1774717543
Write polynomial as irreducible polynomials
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