Why is (x^2+\frac{1}{\sqrt{x}}) not a polynomial?

Correct answer: Because (\frac{1}{\sqrt{x}}) has variable power (-\frac{1}{2})

Direct answer: Option B. A polynomial in x can have only non-negative integer powers of x: 0, 1, 2, 3 and so on. In the expression x^2 + 1/sqrt(x), the first term x^2 is acceptable. But 1/sqrt(x) can be rewritten as 1/x^(1/2) = x^(-1/2). The power -1/2 is negative and fractional, so it is not allowed in a polynomial. Option A is wrong because x^2 is a perfectly valid polynomial term. Option B is correct because it identifies the exact problem: the variable power is -1/2. Option C is wrong because addition is allowed in polynomials; many polynomial terms can be added. Option D is wrong because having two terms is also allowed; a polynomial may have one, two or many terms. Step by step: rewrite the root as a power; move the denominator to the numerator using a negative exponent; inspect -1/2; reject the expression as a polynomial. Memory cue: denominator or root containing the variable often signals an invalid negative or fractional power.