Question Rewrite the following polynomial in standard form. \[ x^{3}+\frac{1}{2} x^{4}+8 \]

To rewrite the polynomial in standard form, we want to arrange the terms in descending order of their degrees. The polynomial you've provided is: \[ x^{3}+\frac{1}{2} x^{4}+8 \] When we reorder it, we start with the term with the highest exponent, which is \(\frac{1}{2} x^{4}\), followed by \(x^{3}\), and then the constant term \(8\). Thus, the standard form of the polynomial is: \[ \frac{1}{2} x^{4} + x^{3} + 8 \]