Question

rewrite the following polynomial in standard form.
$1 - 4x + \frac{x^5}{9} - x^4$

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 \(1 - 4x+\frac{x^{5}}{9}-x^{4}\) from the highest power of \(x\) to the lowest.

Step2: Identify the exponents of each term

• The term \(\frac{x^{5}}{9}\) has an exponent of \(5\) for \(x\).
• The term \(-x^{4}\) has an exponent of \(4\) for \(x\).
• The term \(- 4x\) has an exponent of \(1\) for \(x\).
• The term \(1\) can be thought of as \(1x^{0}\) (since \(x^{0} = 1\)) with an exponent of \(0\) for \(x\).

Step3: Arrange terms in descending order of exponents

Arranging the terms from highest exponent to lowest, we get: \(\frac{x^{5}}{9}-x^{4}-4x + 1\)

Answer:

\(\frac{x^{5}}{9}-x^{4}-4x + 1\)