#### Question

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

`(i) 4x^2 - 3x + 7`

`(ii) y^2+sqrt2`

`(iii) 3sqrtt+tsqrt2`

`(iv) y+2/y`

`(v) x^10+y^3+t^50`

#### Solution

`(i) 4x^2 - 3x + 7`

Yes, this expressions ia polynomial in one variable x.

`(ii) y^2+sqrt2`

Yes, this expression is a polynomial in one variable y.

`(iii) 3sqrtt+tsqrt2`

No. It can be observed that the exponent of variable *t* in term `3sqrtt` is 1/2, which is not a whole number. Therefore, this expression is not a polynomial.

`(iv) y+2/y`

No. It can be observed that the exponent of variable *y* in term `2/y` is -1, which is not a whole number. Therefore, this expression is not a polynomial.

`(v) x^10+y^3+t^50`

No. It can be observed that this expression is a polynomial in 3 variables *x*, *y*, and *t*. Therefore, it is not a polynomial in one variable.