Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer : (i) `3x^2-4x+15` (ii) `y^2+2sqrt(3)` (iii)`3sqrt(x)+sqrt(2)x` (iv) `x-4/x` (v) `x^12 + y^3 + t^50`

Explanation

(i) In `3x^2-4x+15` all the indies of `x` are whole numbers. So, it is a polynomial in one variable `x`.

(ii) In `y^2+2sqrt3` the index of `y` is a whole number. So, it is a polynomial in one variable `y`.

(iii) In `3sqrt(x)+sqrt(2)x`, here the exponent of first term is `1/2`, which is not whole number therefore is it not a polynomial.
(iv) In `x-x/4`, here the exponent of first term is `−1`, which is not whole number, therefore, is it not a polynomial.
(v) In `x^12+y^3+t^50` is not a polynomial in one variable as three variable `x,y and t` occur in it.