Question

Read the following statements
(a) $x^2-5x+\sqrt{2}$ is a polynomial in x.
(b) $4x^2-3\sqrt{x}+7$ is not a polynomial in x.
(c) $\frac{x^2+2x+5}{x+3}(x\ne -3)$ is a rational expression.
(d) $\frac{x^3-5\sqrt{x}-1}{x^2+x+4}$ is not a rational expression.
Correct options is -

• A. acd
• B. abc
• C. abd
• D. abcd

Answer 1

The correct option is D abcd

(a) In each term of the expression, the exponent of $x$ is a non-negative integer.

So, it is a polynomial.
(b) In the second term $(-3\sqrt{x})$ of the expreesion, the exponent of $x$ is $\frac{1}{2}$ which is not a non-negative integer.
So, it is not a polynomial.

(c) Here, in $p\left(x\right)=x^2+2x+5$, the index of x in each terms is a non-negative integer. In $q\left(x\right)=x+3$, the index of $x$ in each term is a non-negative integer. Also as x $\ne$ 3, q(x) $\ne$ 0.

So, it is a rational expression.
(d) In p(x)$=x^3-5\sqrt{x}-1$, the index of x in the second term $(-5\sqrt{x})$ is 1/2 which is not a non-negative integer.
Thus, $p\left(x\right)$ is not a polynomial. Therefore the given expression is not a rational expression.