Which of the following expressions are not polynomials? `x^2+2x^(-2)` (ii) `sqrt(a)x+x^2-x^3` (iii)`3y^3-sqrt(5)y+9` (iv) `a x^(1/2)+ax+9x^2+4` (v) `3x^(-2)+2x^(-1)+4x+5 `

Explanation

To check the given expression is polynomial : it must contain no square roots of variables, no fractional or no negative powers on the variables, and no variables in the denominators of any fractions.

(i) `x^2+2x^(-2)`
In the given expression the power of `x` is negative.
This expression does not satisfy the conditions of a polynomial.
Therefore, this expression is not polynomial.

(ii) `sqrt(a)x+x^2-x^3`
This expression satisfy the conditions of a polynomial.
Therefore, this expression is polynomial.

(iii) `3y^3-sqrt(5)y+9`
This expression satisfy the conditions of a polynomial.
Therefore, this expression is polynomial.

(iv)`ax^(1/2)+ax+9x^2+4`
In the given expression the power of `x` is in fraction.
This expression does not satisfy the conditions of a polynomial.
Therefore, this expression is not polynomial.

(v) `3x^(-2)+2x^(-1)+4x+5`
In the given expression the power of `x` is negative.
This expression does not satisfy the conditions of a polynomial.
Therefore, this expression is not polynomial.