Question

Which of the following are polynomials?

• A. $3+ab+ca+ac+cb$
• B. $a^{-1}+b^{-3}$
• C. $a^3+b^2+c+3$
• D. $-3a^2+\frac{1}{2b^2}$

Answer 1

Answer: (A), (C)

$a^3+b^2+c+3$

An expression containing one or more terms, where the variables have non negative integer exponents is called a polynomial i.e., exponent should be a non negative integer.

$3+ab+ca+ac+cb$
$\text{is a polynomial.}$

$a^{-1}+b^{-3}$
$\text{Here, exponents of a and b}\text{are negative integers.}$
$\therefore \text{It is not a polynomial.}$

$a^3+b^2+c+3\text{is a polynomial.}$

$-3a^2+\frac{1}{2b^2}=-3a^2+2b^{-2}$
$\text{Here, exponent of b is a negative}\text{integer.}$
$\therefore \text{It is not a polynomial.}$