1.

which of the following expressions are polynomials ? Justify your answere, (i) 8 (ii) `sqrt(3x)^(2)-2x (iii) 1-sqrt(5x)` `(iv) (1)/(5x^(-2))+5x+7 (v) ((x-2)(x-4))/(x) (vi) (1)/(x+1)` (vii)` (1)/(7)a^(3)-(2)/(sqrt(3))a^(2)+4a-7 (viii) (1)/(2x)`

Answer» (i) polynomial , because the exponent of the variable of 8 or `8x^(0)` is 0 which is a whole number .
(ii) Not polynomial , because the exponent of the variable of `sqrt(3)x^(2)-2x` is whole number
(iii) Not polynomial ,because the exponent of the variable of `1-sqrt(5)xor 1-sqrt(5)x^(1)/(2))`is `(1)/(2)` which is not whole number.
(iv) polynomial , because the exponent of the variable of `(1)/(5x^(-2))+5x+7=(1)/(5)x^(2)+5x+7,` is a whole number
(v) Not polynomial ,because , the exponent of the variable of `((x-2)(x-4))/(x)=(x^(2)-6x+8)/(x) =x-6+8x^(-1) "is " -1` which is not a whole number .
(vi) Not polynomial as the polynomial is expressed as ` a_(0) ,a_(1)x,a_(2)x,.....,a_(n)x^(n)` are constants ,Now `f(x) =(p(x))/(q(x))` is a rational expression where q(x) `ne` o, p(x) and q(x) are polynomials , Hence ,`(1)/(x+1)` is a rational expression but not not a polynomial .
(vii) Polynomial , because the exponent of the variable of `(1)/(7)a^(3)-(2)/(sqrt(3))a^(2)+4 a-7` is a whole number .
(viii) Not polynomial , because the exponent of the variable of `(1)/(2x) or (1)/(2) x^(-1)` is -1 which is not a whole number.


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