Which of these are polynomials in x? 3x² - √5 x; x^(1/3) + 1; 2/x² + x; -8; (x + 1)(x - 4); √(x³)

Step 1. Polynomials. (a): the powers are $2$ and $1$; $\sqrt{5}$ is only a coefficient. (d): a constant. (e): it multiplies out to $x^2 - 3x - 4$.

Step 2. Not polynomials. (b) has the power $\dfrac{1}{3}$. (c) has $x^{-2}$. (f) is $x^{3/2}$.