Read: Continue with Chapter 5: 5.3.2 through 5.3.3.
Turn in: 5.48, 5.52, 5.55, 5.60, 5.62
- For 5.55, you have the sets $I = \{f(x)a(x) + g(x)b(x)\mid f(x),g(x)\in F[x]\}$ and $J = \{p(x)d(x)\mid p(x)\in F[x]\}$, and you want to show $I = J$. Consider separately showing $I\subseteq J$ and $J\subseteq I$. Both 5.53 and 5.54 are useful.
- We’ve seen the main part of the argument needed for 5.60: if $p(x)$ is a unit then $p(x)q(x) = 1$ for some polynomial $q(x)$, and now we look at what this implies for the degree of $p(x)$ (using 5.35).
Extra practice: 5.51, 5.53, 5.58, 5.59, 5.61
