Question

question
rewrite the following polynomial in standard form.
$-x^{4}+1-\frac{x}{7}$

Explanation:

Step1: Recall standard form of polynomial

The standard form of a polynomial is to write the terms in descending order of their exponents. For a polynomial in one variable \(x\), the standard form is \(a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0\), where \(a_n
eq0\) and \(n\) is the highest degree.

Step2: Identify the degrees of each term

• The term \(-x^4\) has a degree of \(4\).
• The term \(1\) can be written as \(1x^0\), so its degree is \(0\).
• The term \(-\frac{x}{7}\) can be written as \(-\frac{1}{7}x^1\), so its degree is \(1\).

Step3: Arrange terms in descending order of degrees

Arrange the terms from the highest degree to the lowest degree. So we start with the term of degree \(4\) (\(-x^4\)), then the term of degree \(1\) (\(-\frac{x}{7}\)), and then the term of degree \(0\) (\(1\)).

So the polynomial in standard form is \(-x^4-\frac{x}{7}+1\).

Answer:

\(-x^4 - \frac{x}{7} + 1\)