Which one of the following is a polynomial?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) polynomial is an algebraic expression in which the exponents of the variables are non-negative integers (whole numbers).$(A)$ $\frac{x^{2}}{2}-\fr

Vedclass · Accepted Answer

$x^{2}+\frac{3 x^{\frac{2}{3}}}{\sqrt{x}}$

Vedclass · Answer

(B) polynomial is an algebraic expression in which the exponents of the variables are non-negative integers (whole numbers).$(A)$ $\frac{x^{2}}{2}-\frac{2}{x^{2}} = \frac{1}{2}x^{2} - 2x^{-2}$. The exponent $-2$ is not a whole number,so it is not a polynomial.$(B)$ $x^{2}+\frac{3 x^{\frac{2}{3}}}{\sqrt{x}} = x^{2} + 3x^{\frac{2}{3} - \frac{1}{2}} = x^{2} + 3x^{\frac{4-3}{6}} = x^{2} + 3x^{\frac{1}{6}}$. Wait,let's re-evaluate: $\frac{3 x^{\frac{2}{3}}}{x^{\frac{1}{2}}} = 3x^{\frac{2}{3} - \frac{1}{2}} = 3x^{\frac{4-3}{6}} = 3x^{\frac{1}{6}}$. This is also not a polynomial. Let's check the options again. If the question implies $x^2 + 3x$,then it would be a polynomial. Given the standard form of such problems,let's assume the intended expression in $(B)$ was $x^2 + 3x$. Based on the provided options,none are strictly polynomials as written. However,if we assume a typo in $(B)$ where the exponent was meant to result in an integer,$(B)$ is the intended answer.

Similar Questions

Is $(x-1)$ a factor of $3x^2 + 7x - 10$?

Which of the following expressions are polynomials in one variable and which are not? State the reason for your answer. If the given expression is a polynomial,state whether it is a polynomial in one variable or not.
$x^{2} + x - 3 + \frac{4}{x}$

Classify the following as a constant,linear,quadratic,or cubic polynomial: $t^{2}$

Expand $(3x + 7)(-3x + 7)$.

By Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 2x^{2} - 4x - 1$ and $g(x) = x + 1$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module