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.
