Question

Which algebraic expression is a polynomial?

Answers-

4x^2 – 3x + 2 over X

–6x^3 + x^2 – the square root of 5

8x^2 + the square root of X

–2x^4 + 3 over 2x

Answer 1

the answer to this question is
-6x^3+x^2- the square root of 5

Answer 2

`-6x^3+x^2-√(5)`

Explanation:

The general expression of a polynomial of degree n in the variable x is expressed mathematically as:

`P(x)=a_nx^n+a_n_-_1x^(n-1)+...+a_1x^1+a_0x^0`

`n\in N`

Considering the previous definition, let's analyze every expression:

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

It is not polynomial, because the variable is in the denominator.

`-6x^3+x^2-√(5)`

It is a polynomial, because the exponents of the variables are positive integers.

`8x^2+√(x) =8x^2+x^(1/2)`

It is not polynomial, because in the expression there is an exponent that is not a positive integer

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

It is not polynomial, because the variable is in the denominator.