Question

Are the expressions (i) z + 3/z (ii) √3x - 3 polynomials or not? Give reason

Answer 1

No because algebraic expression of form f(x) = a0+a1x+a2x^2+.....a^nx^n , where a0,a1,a2.....,an are real numbers and x is a integer ,then it is said to be polynomial .

Answer 2

Hello friend

Polynomial is an algebraic expression which has non negative integral powers

1. z+3/z

Here in 3/z= 3z^-1, the power of z is -1.
It isn't a non negative integral power. So it isn't a polynomial

2. √3x-3

Here the power of x is 1. So it is a polynomial.
(Note one thing, the co efficient of x is √3. We define a polynomial in terms of the powers of the variable but not the co efficient. So don't consider the co efficient and state it as a polynomial or not)