Polynomial comes from poly- (meaning "many") and also -nomial (in this case an interpretation "term") ... So it says "many terms"


Polynomials through one variable do nice smooth curves:

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A polynomial can have:

constants (like 3, −20, or ½)
variables (like x and also y)
exponents (like the 2 in y2), yet only 0, 1, 2, 3, ...

You are watching: Is 1/x a polynomial

and so on are allowed

that deserve to be combined using addition, subtraction, multiplication and also division ...

... Except ...

... not division by a variable (so something choose 2/x is ideal out)

So:


Also they can have one or more terms, but not one infinite number of terms.

Polynomial or Not?

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These are polynomials:


(Yes, "5" is a polynomial, one term is allowed, and it deserve to be just a constant!)

These space not polynomials

3xy-2 is not, since the exponent is "-2" (exponents can only be 0,1,2,...) 2/(x+2) is not, due to the fact that dividing by a change is not permitted 1/x is no either

But these are allowed:

x/2 is allowed, because you deserve to divide through a constant also 3x/8 for the same factor √2 is allowed, because it is a continuous (= 1.4142...etc)

Monomial, Binomial, Trinomial

There room special names because that polynomials with 1, 2 or 3 terms:

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How do you remember the names? Think cycles!

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There is additionally quadrinomial (4 terms) and also quintinomial (5 terms),but those names room not regularly used.

Variables

Polynomials can have no variable at all


Example: 21 is a polynomial. It has actually just one term, i m sorry is a constant.


Or one variable


Example: x4 − 2x2 + x has actually three terms, however only one change (x)


Or 2 or an ext variables


Example: xy4 − 5x2z has actually two terms, and also three variables (x, y and z)


What is Special around Polynomials?

Because that the strict definition, polynomials are basic to occupational with.

For example we know that:

So you deserve to do too many of additions and multiplications, and also still have a polynomial together the result.

Also, polynomials the one change are straightforward to graph, together they have smooth and constant lines.


Example: x4−2x2+x


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See how nice andsmooth the curve is?


You can additionally divide polynomials (but the an outcome may not be a polynomial).

Degree

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


Example:


4x3 − x + 2 The degree is 3 (the largest exponent the x)

For more facility cases, read degree (of an Expression).

Standard Form

The Standard type for composing a polynomial is to placed the terms with the highest degree first.

See more: Convert 18 Mm Equals How Many Inches, Milimeter To Inches Conversion Chart


Example: placed this in traditional Form: 3x2 − 7 + 4x3 + x6

The highest degree is 6, so the goes first, climate 3, 2 and also then the consistent last:

x6 + 4x3 + 3x2 − 7


You don"t have actually to use standard Form, however it helps.


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