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#1 2024-09-24 02:34:29
- Oculus8596
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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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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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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
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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