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) $y^2+\sqrt{2}$
(iii) $3\sqrt{t}+t\sqrt{2}$
(iv) $y+\frac{2}{y}$
(v) $x^{10}+y^3+t^{50}$

Answer 1

(i) In $4x^2-3x+7$. all the indies of $x$ are whole numbers. So, it is a polynomial in one variable $x$.

(ii) In $y^2+\sqrt{2}$ the index of $y$ is a whole number. So, it is a polynomial in one variable $y$.

(iii) In $3\sqrt{t}+t\sqrt{2}=3t^{\frac{1}{2}}+\sqrt{2}t$, here the exponent of first term is $\frac{1}{2}$, which is not whole number therefore is it not a polynomial.

(iv) In $y+\frac{2}{y}=y+2y^{-1}$, here the exponent of first term is $-1$, which is not whole number, therefore, is it not a polynomial.

(v) In $x^{10}+y^3+t^{50}$ is not a polynomial in one variable as three variable $x,y$ and $t$ occur in it.