Is (\sqrt{11}x^3-5x+2) a polynomial in (x)?

Correct answer: Yes, because (\sqrt{11}) is a real coefficient

In a polynomial in x, the exponents of x must be non-negative integers, while the coefficients may be any real numbers. A coefficient such as √11 is a real constant; it is not a square root of the variable x. Thus the presence of a square-root symbol alone does not make an expression non-polynomial. The number of terms also has no such restriction.

The expression is √11 x^3-5x+2. The powers of x are 3, 1, and 0, all of which are non-negative integers. Its coefficients are √11, -5, and 2, all real numbers. Hence it is a polynomial in x, and option A gives the correct reason. Options B, C, and D confuse coefficients, allowed exponents, or number of terms.