Graphing Polynomials

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 + 3x^2 - 5 is a polynomial.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in f(x) = 5x^4 + 2x^3 + 2x - 7, the degree is 4.

A polynomial of degree n can have at most n solutions (or roots). For example, a polynomial of degree 4 can have at most 4 solutions.

The zeros of a polynomial are the values of x for which the polynomial equals zero. They are also known as the roots of the polynomial.

To find the y-intercept of a polynomial function, evaluate the function at x = 0. The y-intercept is the point (0, f(0)).

The leading coefficient is the coefficient of the term with the highest degree. It affects the end behavior of the polynomial graph.

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials or linear expressions.

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division.

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.