Question

Which of the following expressions are not polynomials :

(i) $x^2+2x^{-2}$

(ii) $\sqrt{a}x+x^2-x^3$

(iii) $3y^3-\sqrt{5}y+9$

(iv) $a{x}^{\frac{1}{2}+ax+9x^2+4}$

(v) $3x^{-2}+2x^{-1}+4x+5$

Answer 1

(i) $x^2+2x^{-2}=x^2+2\times \frac{1}{x^2}=x^2+\frac{2}{x^2}$ : It is not polynomial as it has negative integral power.

(ii) $\sqrt{a}x+x^2-x^3$: It is polynomial.

(iii) $3y^3-\sqrt{5}y+9$ : It is a polynomial.

(iv) $a{x}^{\frac{1}{2}+ax+9x^2+4}$: It is not a polynomial as the degree of $\frac{1}{x^2}$ is an integer.

(v) $3x^{-2}+2x^{-1}+4x+5$: It is not a polynomial as the degree of $x^{-2},x^{-1}$ are negative.