What is polynomial

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Polynomial Rules: What Defines Polynomials?

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Melanie has a BS in physical science and is in grad school for analytics and modeling. Her research is in computational chemistry.

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Polynomial Rules

What are the rules for polynomials? The short answer is that polynomials cannot contain the following: division by a variable, negative exponents, fractional exponents, or radicals.

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What is a polynomial?

A polynomial is an expression containing two or more algebraic terms. They are often the sum of several terms containing different powers (exponents) of variables.

There are some pretty cool things about polynomials. For example, if you add or subtract polynomials, you get another polynomial. If you multiply them, you get another polynomial.

Polynomials often represent a function. And if you graph a polynomial of a single variable, you'll get a nice, smooth, curvy line with continuity (no holes.)

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What does 'polynomial' mean?

The "poly" in polynomial comes from Greek and means "multiple." "Nomial", also Greek, refers to terms, so polynomial means "multiple terms."

The elements of a polynomial

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A polynomial can contain variables, constants, coefficients, exponents, and operators.

Melanie Shebel

What Makes Up Polynomials

A polynomial is an algebraic expression made up of two or more terms. Polynomials are composed of some or all of the following:

• Variables - these are letters like x, y, and b
• Constants - these are numbers like 3, 5, 11. They are sometimes attached to variables, but can also be found on their own.
• Exponents - exponents are usually attached to variables, but can also be found with a constant. Examples of exponents include the 2 in 5² or the 3 in x³.
• Addition, subtraction, multiplication, and division - For example, you can have 2x (multiplication), 2x+5 (multiplication and addition), and x-7 (subtract.)

Rules: What ISN'T a Polynomial

There are a few rules as to what polynomials cannot contain:

Polynomials cannot contain division by a variable.
For example, 2y2+7x/4 is a polynomial, because 4 is not a variable. However, 2y2+7x/(1+x) is not a polynomial as it contains division by a variable.

Polynomials cannot contain negative exponents.
You cannot have 2y-2+7x-4. Negative exponents are a form of division by a variable (to make the negative exponent positive, you have to divide.) For example, x-3 is the same thing as 1/x3.

Polynomials cannot contain fractional exponents.
Terms containing fractional exponents (such as 3x+2y1/2-1) are not considered polynomials.

Polynomials cannot contain radicals.
For example, 2y2 +√3x + 4 is not a polynomial