Question

rewrite the following polynomial in standard form.\\frac{1}{5}x^{3} - 1 + x^{4}\answer attempt 1 out of 2\
answer:\

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written with the terms in descending order of their exponents. So we need to arrange the terms of the polynomial \(\frac{1}{5}x^{3}-1 + x^{4}\) by the degree of each term.

Step2: Identify the degrees of each term

• The term \(x^{4}\) has a degree of 4.
• The term \(\frac{1}{5}x^{3}\) has a degree of 3.
• The term \(- 1\) (which can be thought of as \(-1x^{0}\)) has a degree of 0.

Step3: Arrange terms in descending order of degrees

Arrange the terms from highest degree to lowest degree. So we start with the term of degree 4 (\(x^{4}\)), then the term of degree 3 (\(\frac{1}{5}x^{3}\)), and then the term of degree 0 (\(-1\)).

So the polynomial in standard form is \(x^{4}+\frac{1}{5}x^{3}-1\).

Answer:

\(x^{4}+\frac{1}{5}x^{3}-1\)