*Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.*

- $\rhd$ 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?
- $\rhd$ Find roots a of cubic polynomial (17:00) Find the roots and sketch a graph of $f(x)=2x^3-7x^2-3x+8$
- $\rhd$ 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 $3i$.

**Rational Root Theorem:**

- $\rhd$ Rational root theorem (6:01) Find the possible rational roots of $f(x)=2x^3-12x^2+22x-12$