Special Kinds of Polynomials at a Glance

We know what you're thinking. Aren't all polynomials special? Aw. That's sweet, but stop kissing up.

There are special names for polynomials with certain numbers of terms.

A monomial is a polynomial with only one term, such as 3x, 4xy, 7, and 3x²y³⁴.
A binomial is a polynomial with exactly two terms, such as x + 3, 4x² + 5x, and x + 2y⁷.
A trinomial is a polynomial with exactly three terms, such as 4x⁴ + 3x³ – 2.

You can remember these three because a tricycle has three wheels, a bicycle has two wheels, and a monocycle has...man, that almost worked.

Another special kind of polynomial is a quadratic polynomial, which is a polynomial of degree 2. Yes, "quad" usually means "4," but bear with us.

A quadratic polynomial looks like ax² + bx + c, where a, b, and c are real numbers and a isn't zero (if a were zero, the polynomial would only have degree 1).

A 2nd degree polynomial is "quadratic." Shouldn't it be "biratic?" What's the good of these numerical prefixes if they're only going to keep changing them on us?

A valid question. The answer? "Quad" also means "square." Oooh...sneaky.

In a single-variable polynomial of degree 2, we're squaring the variable, so it makes sense to think of that polynomial as "quadratic." We'll cross our fingers and hope "quad" doesn't also mean a third thing.

The following polynomials are quadratic.