2.1 Foundations of Polynomials

(i) $x^2 + \sqrt{x}$: The term $\sqrt{x}$ can be written as $x^{1/2}$. Since $1/2$ is not a whole number, this is NOT a polynomial.

(ii) $\sqrt{3}x^2 + 5x$: The variable $x$ has exponents 2 and 1 (both whole numbers). The coefficient $\sqrt{3}$ is a real number (allowed). Thus, it IS a polynomial. Highest power is 2, so Degree = 2.

(iii) $t^2 + 5t^{-1}$: The term $t^{-1}$ has a negative exponent (-1 is not a whole number). Thus, it is NOT a polynomial.

(iv) 0: This is the Zero Polynomial. It is a polynomial, but its degree is undefined.