Question

Which of the following expressions is a polynomial in one variable?

• A. $x^{\pi }+x^{-2}$
• B. $\pi x^3+3x^2+9$
• C. $2x^4+4x^{3/2}+2$
• D. $3x^2+4xy+\sqrt{2}$

Answer 1

The correct option is B $\pi x^3+3x^2+9$

i) $x^{\pi }+x^{-2}$ is not a polynomial because the exponents $\pi$ and $-2$ are not whole numbers.
ii) $\pi x^3+3x^2+9$ is a polynomial as each exponent is a whole number.
iii) $2x^4+4x^{3/2}+2$ is not a polynomial as one of the exponents, $\frac{3}{2}$, is not a whole number.
iv) $3x^2+4xy+\sqrt{2}$ is a polynomial in two variables, $x$ and $y$.