# At a Glance - Special Kinds of Polynomials

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 3*x*, 4*xy*, 7, and 3*x*^{2}*y*^{34}.

- A
**binomial**is a polynomial with exactly two terms, such as*x*+ 3, 4*x*^{2}+ 5*x*, and*x*+ 2*y*^{7}.

- A
**trinomial**is a polynomial with exactly three terms, such as 4*x*^{4}+ 3*x*^{3}– 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* ax*^{2} + *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.

*x*^{2 }- -4
*x*^{2}+ 8

- 5
*x*^{2}+ 6*x*– 1

The following polynomials are *not* quadratic.

*x*+ 5

*x*^{4}+ 6*x*^{2}+ 2

- 8

#### Exercise 1

Is the following polynomial a monomial, binomial, or trinomial?

45*x*^{7} – 8*x*^{2} + 4*x*

#### Exercise 2

Is the following polynomial a monomial, binomial, or trinomial?

*x*

#### Exercise 3

Is the following polynomial a monomial, binomial, or trinomial?

5*x*^{5} + 4*x*

#### Exercise 4

Is the following polynomial a monomial, binomial, or trinomial?

5

#### Exercise 5

Is the following polynomial a quadratic?

5*x*^{2}

#### Exercise 6

Is the following polynomial a quadratic?

*x*^{4} + 3*x* – 2

#### Exercise 7

Is the following polynomial a quadratic?

*x* + 4

#### Exercise 8

Is the following polynomial a quadratic?

-4.5*x*^{2} + 4*x* – 3.2