Get expert advice and community support for your questions on IDNLearn.com. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.
Sagot :
To solve the question of identifying which expressions are monomials, let's understand what a monomial is. A monomial is an algebraic expression that is a single term consisting of a constant and/or a variable raised to a non-negative integer exponent. Monomials do not involve addition, subtraction, or variables in denominators or under radicals.
Let's analyze each option given:
A. [tex]\( x \)[/tex]
This is a single variable with the exponent 1 (which is a non-negative integer). Therefore, [tex]\( x \)[/tex] is a monomial.
B. [tex]\( \sqrt{x} \)[/tex]
The square root of [tex]\( x \)[/tex] can be written as [tex]\( x^{1/2} \)[/tex]. Since the exponent is not an integer, [tex]\( \sqrt{x} \)[/tex] is not a monomial.
C. 6
This is a constant term, which can be considered as [tex]\( 6 \cdot x^0 \)[/tex] (where the exponent is 0, a non-negative integer). Therefore, 6 is a monomial.
D. [tex]\( x + 1 \)[/tex]
This expression involves the addition of two terms. Monomials do not involve addition or subtraction, hence [tex]\( x + 1 \)[/tex] is not a monomial.
E. [tex]\( -4 x^3 \)[/tex]
This is a single term where the variable [tex]\( x \)[/tex] is raised to the power of 3 (a non-negative integer) and multiplied by a constant. Hence, [tex]\( -4 x^3 \)[/tex] is a monomial.
F. [tex]\( \frac{5}{x} \)[/tex]
This can be written as [tex]\( 5x^{-1} \)[/tex]. Since the exponent is negative, [tex]\( \frac{5}{x} \)[/tex] is not considered a monomial.
Based on this analysis, the expressions that are monomials are:
- A. [tex]\( x \)[/tex]
- C. 6
- E. [tex]\( -4 x^3 \)[/tex]
Therefore, the monomials can be listed as:
```
['A', 'C', 'E']
```
Let's analyze each option given:
A. [tex]\( x \)[/tex]
This is a single variable with the exponent 1 (which is a non-negative integer). Therefore, [tex]\( x \)[/tex] is a monomial.
B. [tex]\( \sqrt{x} \)[/tex]
The square root of [tex]\( x \)[/tex] can be written as [tex]\( x^{1/2} \)[/tex]. Since the exponent is not an integer, [tex]\( \sqrt{x} \)[/tex] is not a monomial.
C. 6
This is a constant term, which can be considered as [tex]\( 6 \cdot x^0 \)[/tex] (where the exponent is 0, a non-negative integer). Therefore, 6 is a monomial.
D. [tex]\( x + 1 \)[/tex]
This expression involves the addition of two terms. Monomials do not involve addition or subtraction, hence [tex]\( x + 1 \)[/tex] is not a monomial.
E. [tex]\( -4 x^3 \)[/tex]
This is a single term where the variable [tex]\( x \)[/tex] is raised to the power of 3 (a non-negative integer) and multiplied by a constant. Hence, [tex]\( -4 x^3 \)[/tex] is a monomial.
F. [tex]\( \frac{5}{x} \)[/tex]
This can be written as [tex]\( 5x^{-1} \)[/tex]. Since the exponent is negative, [tex]\( \frac{5}{x} \)[/tex] is not considered a monomial.
Based on this analysis, the expressions that are monomials are:
- A. [tex]\( x \)[/tex]
- C. 6
- E. [tex]\( -4 x^3 \)[/tex]
Therefore, the monomials can be listed as:
```
['A', 'C', 'E']
```
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.