- $\rhd$ 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.
- $\rhd$ Quadratics and the Fundamental Theorem of Algebra (6:34) What does the Fundamental Theorem of Algebra say about the polynomial $5x^2+6x+5$? Find its roots and check its graph.
- $\rhd$ The number of possible real roots of a polynomial (3:45) How many real roots can a degree-7 polynomial have?
- $\rhd$ 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 (3:50) $f$ has degree $3$, the leading coefficient is $5$, and the roots of $f$ are precisely $-3$, $2$, $5$.
- $\rhd$ Finding a polynomial f that fits the given data (2:57) $f$ has degree $3$, the roots of $f$ are precisely $1$, $-2$, $3$, and $f(0)=-12$.
- $\rhd$ 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 $3i$.
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