Read: Sections 5.3.1 and 5.3.2.
Problems to Try: 5.39, 5.40, 5.41, 5.44, 5.45, 5.46, 5.48, 5.52, 5.55
- 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.
Extra practice: 5.41, 5.51, 5.53