Question

rewrite the following polynomial in standard form.
$-x^4 + 1 - \frac{1}{10}x^2$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written with terms in descending order of degree. The degree of a term is the exponent of the variable.

Step2: Identify degrees of each term

• For the term $-x^4$, the degree is 4.
• For the term $1$, we can think of it as $1x^0$, so the degree is 0.
• For the term $-\frac{1}{10}x^2$, the degree is 2.

Step3: Arrange terms in descending order of degree

Arrange the terms from highest degree to lowest degree. So we start with the term of degree 4, then degree 2, then degree 0.
So the polynomial $-x^4 + 1-\frac{1}{10}x^2$ in standard form is $-x^4-\frac{1}{10}x^2 + 1$.

Answer:

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