Which of the following expression are polynomial .if not give reason :
(i) ` (1)/( x^(2)) +3x -4`
(ii) ` x^(2) (x-1) `
(iii) ` (1)/(x) (x+5) `
(iv) ` (1)/(x^(-2) ) +(1)/( x^(-1)) +7`
(v) ` sqrt (5) x ^(2) + sqrt 3x +sqrt2`
(vi ) ` m^(2) -3sqrt (m) +7m-10`

Answer

`(1)/(x^(2)) +3x -4 ` is not a polynomial .Since the exponent of ` x^(2) ` is not a whole number but it is `((1)/(x^(2)) =x^(-2))` negative numbers.
(ii) ` x^(2) (x-1) ` is a polynomial
(iii) `((1)/(x) =x^(-1))` negative number.
(iv) (Since ` (1)/9x^(-2) =x^(2) and (1)/( x^(-1))=x ) `
(v) ` sqrt 5x^(2) +sqrt 3x +sqrt2`
(vi) ` (3sqrtm=m^(1//3)`