$\rhd$ The Fundamental Theorem of Algebra (5:33) A discussion on the fundamental theorem of algebra relating the degree of a polynomial and the number of real and non-real roots.
$\rhd$ Sketching the graph of a polynomial (23:04) Graph $f(x)=x^3-3x^2-2x+6$ by finding the roots of $f$ in exact form and its complete factorization.
$\rhd$ Finding a polynomial f that fits the given data (4:53) $f$ has degree $4$, and the leading coefficient is $-3$. The coefficients of $f$ are all real. The polynomial $f$ has roots $1$, $2$ and $3i$.