Melanie has a BS in physical science and also is in grad institution for analytics and modeling. She also runs a YouTube channel: The Curious Coder.

You are watching: Which expression is not a polynomial


Polynomial Rules

What space the rules because that polynomials? The brief answer is the polynomials cannot save on computer the following: department by a variable, an adverse exponents, fountain exponents, or radicals.

What is a polynomial?

A polynomial is one expression containing two or more algebraic terms. They are frequently the sum of numerous terms having different powers (exponents) that variables.There space some quite cool things around polynomials. For example, if you include or subtract polynomials, friend get another polynomial. If you multiply them, you get another polynomial.Polynomials regularly represent a function. And also if girlfriend graph a polynomial that a single variable, you'll gain a nice, smooth, curvy line v continuity (no holes.)

What does 'polynomial' mean?

The poly in polynomial comes from Greek and means multiple. Nomial, which is additionally Greek, refers to terms, for this reason polynomial method multiple terms.


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

Melanie Shebel

What renders Up Polynomials

A polynomial is one algebraic expression consisted of of 2 or an ext terms. Polynomials are composed of part or every one of the following:

Variables - these space letters prefer x, y, and also bConstants - these are numbers favor 3, 5, 11. They are periodically attached to variables however are additionally found on their own.Exponents - exponents are usually attached to variables yet can additionally be found with a constant. Examples of exponents encompass 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 also x-7 (subtraction.)

Rules: What ISN'T a Polynomial

There space a few rules as to what polynomials cannot contain:Polynomials cannot contain department by a variable.For example, 2y2+7x/4 is a polynomial due to the fact that 4 is no a variable. However, 2y2+7x/(1+x) is no a polynomial together it contains department by a variable.Polynomials cannot contain negative exponents.You cannot have 2y-2+7x-4. An unfavorable exponents room a kind 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 include fractional index number (such together 3x+2y1/2-1) space not considered polynomials.Polynomials can not contain radicals.For example, 2y2 +√3x + 4 is no a polynomial.


How to discover the degree of a polynomial

To find the polynomial degree, write down the terms of the polynomial in descending stimulate by the exponent. The term whose exponents include up to the highest possible number is the top term. The sum of the index number is the degree of the equation.Example: number out the level of 7x2y2+5y2x+4x2.Start by adding the index number in each term.The index number in the an initial term, 7x2y2, space 2 (from 7x2) and 2 (from y2) which add up to four.The second term (5y2x) has actually two exponents. They space 2 (from 5y2) and also 1 (from x, this is since x is the very same as x1.) The index number in this term include up to three.The last term (4x2) only has one exponent, 2, for this reason its level is just two.Since the an initial term has the highest degree (the 4th degree), the is the top term. The level of this polynomial is four.

Test your Knowledge

For every question, pick the finest answer. The answer vital is below.

What is/are the constant(s) in 3y² + 2x + 5?325All that the aboveWhat is/are the term(s) in 3y² + 2x + 5?3y²2x5All that the aboveWhat is/are the coefficient(s) in 3y² + 2x + 5?325Both 3 & 2Which the the adhering to is a variable in 3y² + 2x + 5?²x5

Answer Key

5All of the aboveBoth 3 & 2x

Different species of polynomials

There are different ways polynomials deserve to be categorized. They are often named for the degree of the polynomial and the number of terms that has. Here are some examples:

Monomials - These space polynomials containing only one term ("mono" way one.) 5x, 4, y, and also 5y4 are all instances of monomials.Binomials - These space polynomials that contain just two state ("bi" means two.) 5x+1 and also y-7 are instances of binomials.Trinomials - These room polynomials the contain 3 terms ("tri" meaning three.) 2y+5x+1 and y-x+7 are examples of trinomials.

There room quadrinomials (four terms) and also so on, however these space usually just called polynomials regardless of the number of terms castle contain. Polynomials can have one infinite variety of terms, therefore if you're not sure if it's a trinomial or quadrinomial, friend can call it a polynomial.A polynomial can additionally be called for the degree. If a polynomial has a degree of two, that is often referred to as a quadratic. If it has a level of three, it can be dubbed a cubic. Polynomials through degrees higher than three aren't usually called (or the surname are seldom used.)You have the right to do many operations ~ above polynomials. Here, the FOIL method for multiply polynomials is shown.


There room a number of operations that deserve to be excellent on polynomials. Below the FOIL technique for multiply polynomials is shown.

Melanie Shebel

Operations top top Polynomials

Now the you know what renders up a polynomial, it's a good idea to gain used to working through them. If you're acquisition an algebra course, opportunities are you'll it is in doing work on polynomials together as adding them, individually them, and even multiplying and dividing polynomials (if you're not currently doing so.)

© 2012 Melanie Palen


Miltone on may 23, 2020:

Excellent explanation. Thanks.

Naresh on may 12, 2020:

Why polynomials don't have negative exponents? i am not able come find any type of reason for this.

Ojasva on may 11, 2020:

What is negative exponent or fractional exponent change called, if no monomial or polynomial

Vin Chauhun indigenous Durban on may 07, 2012:

just looking in ~ those equations brought about my brain to breakout right into a civil war. :)

Moon Daisy indigenous London top top April 18, 2012:

A great hub. Ns love maths, but I'm a small rusty top top the terminology. Therefore thanks!

cardelean from Michigan top top April 17, 2012:

Excellent guide. I have actually a emotion I'll it is in referring earlier to it as my kids get a small older! :)

Sondra native Neverland top top April 15, 2012:

Melbel I will not take her quiz due to the fact that I already know I will certainly fail hehe Math never was mine thing. Oddly sufficient my daughter (11) is a mathematics genius and I am going to let her review this tomorrow. She will love it :)

Teresa Coppens native Ontario, Canada on April 15, 2012:

Another great math hub Mel. Very useful for those struggling through these concepts and also there are plenty of out there including parents struggling to aid their children in grades 6 to 8 with simple algebra.

Xavier Nathan native Isle of man on April 15, 2012:

A really nice treatment of this topic and also I think you should additionally create a YouTube channel and also make short videos to go through each of your hubs and also before long you will have actually lots of math students following you. Good work.

Jessee R native Gurgaon, India ~ above April 15, 2012:

Nice basic outlay about polynomials... Informative

Zulma Burgos-Dudgeon from uk on April 15, 2012:

I have to confess, I acquired confused and also frustrated after the an initial paragraph. Math and I don't obtain on.

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But from what I might comprehend this appears to it is in a an excellent hub and also I don't doubt you'll it is in helping lots of civilization who possibly didn't know their instructor's explanation.