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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

Textbook Definition of Monomial

A monomial in one variable is the product of a constant and a variable raised to a positive integer power. A monomial is of the form ax^k, where a is a constant, x is a variable, and k => 0 is an integer. The constant a is called the coefficient of the monomial. If a does not equal 0, then k is called the degree of the monomial.

For each question, tell if the expression is a monomial.

If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not.

A. 2x^3

B. 8/x

C. -2x^(-3)

D. 8x/y

E. x^2 + y^2

A is a monomial. The variable is x. The coefficient is 2 and power is 3.

B is not a monomial. You see, 8/x can be written as 8x^(-1). The negative power indicates that it is not a monomial.

C. C is not a monomial for the same reason that B is not a monomial.

D is not a monomial for the same reason that B and C are not a monomial.

E is not a monomial. It is a binomial.

Do you agree with my reasoning and answers?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,583

A, B and C exactly right.

For D and E I would say the presence of another variable y is a reason. Also E has a + element as well.

Further thought about D. If we consider a = 8/y and k = 1 then it is monomial. I'm regarding y as a fixed value rather than a variable. Why not?

Bob

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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

Bob wrote:

A, B and C exactly right.

For D and E I would say the presence of another variable y is a reason. Also E has a + element as well.

Further thought about D. If we consider a = 8/y and k = 1 then it is monomial. I'm regarding y as a fixed value rather than a variable. Why not?

Bob

You said:

"Further thought about D. If we consider a = 8/y and k = 1 then it is monomial. I'm regarding y as a fixed value rather than a variable."

I don't know what you mean here.

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