Answer:
The expression which is a polynomial is:
[tex]-6x^3+x^2-\sqrt{5}[/tex]
Step-by-step explanation:
A polynomial expression is a expression of the form:
[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+........+a_1x+a_0[/tex]
where n belong to non-negative integers and [tex]a_i's[/tex] are real numbers.
1)
[tex]4x^2-3x+\dfrac{2}{x}[/tex]
This is not a polynomial because the third term:
[tex]\dfrac{2}{x}=2x^{-1}[/tex] has a negative poswer of x which violates the definition of polynomial.
2)
[tex]-6x^3+x^2-\sqrt{5}[/tex]
In this each of the term satisfy the definition of polynomial and hence the expression is a polynomial expression.
3)
[tex]8x^2+\sqrt{x}[/tex]
Here the second term is not a integer power and hence violate the definition of polynomial.
4)
[tex]-2x^4+\dfrac{3}{2x}[/tex]
which could also be written as:
[tex]-2x^4+\dfrac{3}{2}x^{-1}[/tex]
Here the second term contain a negative power of x and hence is not a polynomial.
