Question

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

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

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

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

Answer 1

Polynomial:

Polynomial is an algebraic expression in which the variable have the powers only whole numbers in all terms.

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

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.

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

$\Rightarrow 3t^{\frac{1}{2}}+t\sqrt{2}$

It is not a polynomial because exponent of variable $t$ is not a whole number in the term $3\sqrt{t}$.