Definition of a Polynomial

Option B is correct. In the original form (x² + 4)/(x + 1), the variable x occurs in the denominator. Equivalently, the expression involves division by a variable-containing quantity, so it cannot be written as a finite sum of terms with only non-negative integer powers of x and constant coefficients. The denominator also creates a restriction x ≠ -1. Options A and D are ordinary polynomials with non-negative integer powers. Option C is also a polynomial because √2 is merely a constant coefficient of x²; irrational coefficients are allowed. The phrase “in its original form” matters: a rational expression may simplify in special cases, but it must be classified as written. Therefore B is the only valid answer.

Here, \(x^0=1\), so the expression becomes \(1+3x^2-2x\). The highest power of \(x\) is \(2\); therefore, the degree of the polynomial is \(2\). The term containing \(x^0\) has degree \(0\), but it is not the highest power. Exam tip: Simplify the polynomial first, then identify the greatest exponent of the variable.