Question

Which algebraic expression is a polynomial?

Answer 1

Answer: The answer is B.

Step-by-step explanation: "Poly" means "many", and "nomial", in this case, meaning "term".

B is the only one with 3 or more different terms.

(negative number, whole number, two unknowns, and a square root)

Answer 2

The expression which is a polynomial is:

`-6x^3+x^2-√(5)`

Explanation:

A polynomial expression is a expression of the form:

`f(x)=a_nx^n+a_(n-1)x^(n-1)+........+a_1x+a_0`

where n belong to non-negative integers and
`a_i's` are real numbers.

1)

`4x^2-3x+(2)/(x)`

This is not a polynomial because the third term:

`(2)/(x)=2x^(-1)` has a negative poswer of x which violates the definition of polynomial.

2)

`-6x^3+x^2-√(5)`

In this each of the term satisfy the definition of polynomial and hence the expression is a polynomial expression.

3)

`8x^2+√(x)`

Here the second term is not a integer power and hence violate the definition of polynomial.

4)

`-2x^4+(3)/(2x)`

which could also be written as:

`-2x^4+(3)/(2)x^(-1)`

Here the second term contain a negative power of x and hence is not a polynomial.