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# Polynomials

A polynomial looks like this:
 example of a polynomial this one has 3 terms

 constants (like 3, -20, or ½) variables (like x and y) exponents (like the 2 in y2) but they can only be 0, 1, 2, 3, ... etc

That can be combined using:

 + - × addition, subtraction and multiplication, ... ... but not division!

Those rules keeps polynomials simple, so they are easy to work with!

## Polynomials or Not?

These are polynomials:

• 3x
• x - 2
• 3xyz + 3xy2z - 0.1xz - 200y + 0.5

And these are not polynomials

• 2/(x+2) is not, because dividing is not allowed
• 3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

But this is allowed:

• x/2 is allowed, because it is also (½)x (the constant is ½, or 0.5)
• also 3x/8 for the same reason (the constant is 3/8, or 0.375)

## Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

 How do you remember the names? Think cycles!

(There's also quadrinomial (4 terms) and quintinomial (5 terms), but these are not often used)

## Lots and Lots of Terms

Polynomials can have as many terms as needed, but not an infinite number of terms.

## What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.

For example we know that:

So you can do lots of additions and multiplications, and still have a polynomial as the result.

## Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

 The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).