Polynomials

What is a Polynomial?

A polynomial is an algebraic expression where the exponents of all variables are whole numbers. You classify polynomials based on their degree. The degree is the highest power of the variable in the expression.

• Linear Polynomial: Degree 1. Example: $p(x) = 2x + 3$

• Quadratic Polynomial: Degree 2. Example: $p(x) = x^2 – 4x + 4$

• Cubic Polynomial: Degree 3. Example: $p(x) = x^3 – 2x^2 + x – 1$

The Geometrical Meaning of Zeroes

A “zero” of a polynomial is simply a value of $x$ that makes the entire expression equal $0$.

If you plot a polynomial on a graph, the zeroes are the exact coordinates where the line or curve crosses the horizontal x-axis. A polynomial of degree $n$ can intersect the x-axis at most $n$ times. Therefore, a quadratic polynomial has a maximum of two zeroes.