Question

question
rewrite the following polynomial in standard form.
$\displaystyle -\frac{x^{4}}{6} + x^{2} - 9x^{3} - 1$

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 \(-\frac{x^{4}}{6}+x^{2}-9x^{3}-1\) from the highest power of \(x\) to the lowest.

Step2: Identify the exponents of each term

• The term \(-\frac{x^{4}}{6}\) has an exponent of \(4\) for \(x\).
• The term \(-9x^{3}\) has an exponent of \(3\) for \(x\).
• The term \(x^{2}\) has an exponent of \(2\) for \(x\).
• The term \(- 1\) (which can be written as \(-1x^{0}\)) has an exponent of \(0\) for \(x\).

Step3: Arrange the terms in descending order of exponents

Arranging the terms from highest exponent to lowest, we get: \(-\frac{x^{4}}{6}-9x^{3}+x^{2}-1\)

Answer:

\(-\frac{x^{4}}{6}-9x^{3}+x^{2}-1\)