- Topics At a Glance
- Exponents
- Negative Exponents
- Fractional Exponents
- Irrational Exponents
- Variables as Exponents
**Defining Polynomials**- Degrees of a Polynomial
- Multivariable Polynomials
- Degrees of Multivariable Polynomials
**Special Kinds of Polynomials**- Evaluating Polynomials
- Roots of a Polynomial
- Combining Polynomials
- Multiplying Polynomials
- Multiplication of a Monomial and a Polynomial
- Multiplication of Two Binomials
- Special Cases of Binomial Multiplication
- General Multiplication of Polynomials
- We'll Divide Polynomials Later!
- Factoring Polynomials
- The Greatest Common Factor
- Recognizing Products
- Trial and Error
- Factoring by Grouping
- Summary
- Introduction to Polynomial Equations
- Solving Polynomial Equations
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

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 degree 2 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 does make 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 is quadratic?

5*x*^{2}

Exercise 6

Is the following polynomial is quadratic?

*x*^{4} + 3*x* - 2

Exercise 7

Is the following polynomial is quadratic?

*x* + 4

Exercise 8

Is the following polynomial is quadratic?

-4.5*x*^{2} + 4*x* - 3.2