1.10.6 Polynomials

Problem: Decompose the polynomial \( g(x)=1+g_{1} x+ \) \( +g_{2} x^{2}+g_{3} x^{3}+g_{4} x^{4}+x^{5} \in \mathbb{Z}_{2}[x] \) into a product of irreducible factors. \[ g_{1} g_{2} g_{3} g_{4}=1100 \text {. } \]