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#1 2024-09-24 02:34:29

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

Monomial Expression

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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#2 2024-09-24 04:09:53

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

Re: Monomial Expression

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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#3 2024-09-24 12:08:27

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

Re: Monomial Expression

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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