Question

Which of the following expression are polynomials in one variable and which not ? State reason for your answe.
$\left(i\right)4x^2-3x+7$
$\left(ii\right)y^2+\sqrt{2}$

$\left(iii\right)3\sqrt{1}+1\sqrt{2}$

$\left(iv\right)y+\frac{2}{y}$

Answer 1

Polynomial:

A polynomial is an algebraic expression in which the power of the variable of all terms are whole numbers.

$\left(i\right)4x^2-3x+7$

It is a polynomial in one variable because there is just one variable $x$ and the exponent of $x$ is a whole number in all the terms.

$\left(ii\right)y^2+\sqrt{2}$

It is a polynomial in one variable because there is just one variable $y$ and the exponent of $y$ is a whole number in all the terms.

$iii)3\sqrt{1}+1\sqrt{2}$

Since all the terms are constants. So it is a Constant polynomial.

$iv)y+\frac{2}{y}$

$\Rightarrow y+2y^{-1}$

It is not a polynomial because exponent of variable $y$ is not a whole number in second term.