Let $$f(x) = x^2+2x+3 \quad\hbox{and}\quad g(x) = 4x^3-5x^2+4x+1$$
For brevity let's write $\hbox{deg}(p)$ for the degree of a polynomial $p$. So in the above example, $\hbox{deg}(f) = 2$ and $\hbox{deg}(g) = 3$. You can answer the following questions without actually computing the indicated functions.


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