Suppose $f$ is a polynomial of degree $m$, and $g$ is a polynomial of degree $n$. For simplicity, let's also suppose that $$m > n.$$ (Ponder what the complications would be if we did not make that assumption.)


$\hbox{deg}(f+g)$ .
$\hbox{deg}(f-g)$ .
$\hbox{deg}(fg)$ .
$\hbox{deg}(f\circ g)$ .
$\hbox{deg}(g\circ f)$ .