Which expression is not a polynomial in x because √(x² + 1) is present?

Correct answer: √(x² + 1) + x

The defining test is whether the variable appears only with non-negative integer powers in a finite sum. Option C contains √(x² + 1), in which the variable occurs inside a square root applied to a non-monomial expression. This is not a polynomial term, so √(x² + 1) + x is not a polynomial in x. Option A is a polynomial with powers 2 and 0. Option B is also a polynomial: √2 is a real constant coefficient, not a variable power. Option D has powers 4 and 2 and is plainly a polynomial. Thus option C is correct. The important distinction is that a root of a constant, such as √2, is allowed as a coefficient; a variable-containing radical is a different kind of expression.