Question

Which of the following is/are a polynomial?

• A. $3x^3+9x^{-1}+9$
• B. $\sqrt{5}{x}^2+5x-7$
• C. $8x^7-x^2+2\sqrt{3}$
• D. $5\sqrt{x}+2x^2-4$

Answer 1

Answer: (B), (C)

$8x^7-x^2+2\sqrt{3}$

In $3x^3+9x^{-1}+9$, the exponent of the second term is $-1,$ which is not a whole number. Therefore it is not a polynomial.

In $\sqrt{5}{x}^2+5x-7$, exponent of each term is a whole number and also coefficients are real. Therefore, it is a polynomial.

Similarly, $8x^7-x^2+2\sqrt{3}$ is also a polynomial.

In $5\sqrt{x}+2x^2-4x+5$, the exponent in first term is not a whole number. Therefore, it is not a polynomial.