Zeroes of Polynomial Functions

The fundamental theorem states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

To construct a polynomial from given zeros, set $x$ equal to each zero, move everything to one side, then multiply each resulting equation.

The factored form of a polynomial reveals its zeros, which are defined as points where the function touches the $x$-axis.

Each solution to a polynomial, expressed as $x= \frac {p}{q}$, must satisfy that $p$ and $q$ are integer factors of $a_0$ and $a_n$, respectively.

The rule of signs gives an upper bound number of positive or negative roots of a polynomial.