Question

rewrite the following polynomial in standard form.
$-1 - \frac{x^4}{2} - 3x^2$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written in descending order of the exponents of the variable. So we need to arrange the terms of the polynomial \(-1 - \frac{x^{4}}{2}- 3x^{2}\) by the degree of \(x\) in descending order.

The degree of \(-\frac{x^{4}}{2}\) is \(4\), the degree of \(- 3x^{2}\) is \(2\) and the degree of \(-1\) (which can be written as \(-1x^{0}\)) is \(0\).

Step2: Arrange the terms

Arrange the terms from highest degree to lowest degree. So the term with \(x^{4}\) comes first, then the term with \(x^{2}\), then the constant term.

So the polynomial in standard form is \(-\frac{x^{4}}{2}- 3x^{2}-1\)

Answer:

\(-\frac{x^{4}}{2}- 3x^{2}-1\)