Question

Which of the following are polynomials?

• A. $2x^3+2x+4x^{\frac{3}{2}}$
• B. $4x^2+6x+4x^3+2x^2$
• C. $3x^2+2x+4x^9$
• D. $3x^2+2x+4x^{-9}$

Answer 1

Answer: (B), (C)

$3x^2+2x+4x^9$

In a polynomial the powers of the variables must be whole numbers.

Clearly $3x^2+2x+4x^9$ and $4x^2+6x+4x^3+2x^2$ are polynomials.

But in case of $2x^3+2x+4x^{\frac{3}{2}}$ , power of variable $x$ is $\frac{3}{2}.$ Which is not a whole numeber. Hence it is not a polynomial.
Similarly, in the expression $3x^2+2x+4x^{-9}$ is not a polynomial because power of $x$ is $-9$.