Let $f(x)$ be degree $n$ polynomial, with $n+1$ nonzero monomial, i.e., all coefficients nonzero (for example if $n = 3$, then we could have $3x^3 + 2x^2 + x + 10$)
Let $g(x)$ be any polynomial of degree $m$, (which may have some coefficients equal to $0$; e.g., f.e, with $m = 4$, we could take $4x^4 + 2$
Let $h(x) = f(x) * g(x)$
What can be said about the number of terms in $h(x)$? Can it be less than the number of terms in f(x) or g(x)?