Question

question
rewrite the following polynomial in standard form.
$-x^4 + 1 - \frac{1}{10}x^2$
answer attempt 1 out of 2
answer:

Explanation:

Step1: Recall standard form of polynomial

The standard form of a polynomial is written in descending order of the exponents of the variable. 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 \(n\) is the highest power (degree) of \(x\) and \(a_n
eq0\).

Step2: Identify the terms and their degrees

Given polynomial: \(-x^4+1-\frac{1}{10}x^2\)

• The term \(-x^4\) has degree \(4\)
• The term \(1\) (which can be written as \(1x^0\)) has degree \(0\)
• The term \(-\frac{1}{10}x^2\) has degree \(2\)

Step3: Rearrange terms in descending order of degrees

Arrange the terms from highest degree to lowest degree.
So, the highest degree term is \(-x^4\) (degree \(4\)), then the next is \(-\frac{1}{10}x^2\) (degree \(2\)), and then the constant term \(1\) (degree \(0\)).

Putting them together, the polynomial in standard form is:
\(-x^4-\frac{1}{10}x^2 + 1\)

Answer:

\(-x^4-\frac{1}{10}x^2 + 1\)