Question

Write the polynomial in standard form. Then find its degree and the leading coefficient.
3 w minus w Superscript 6 Baseline plus 0.4 w cubed minus 9.53w−w6+0.4w3−9.5
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Part 1
Write the polynomial in standard form. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The standard form of the polynomial is enter your response here.
​(Use integers or decimals for any numbers in the​ expression.)
B.
The polynomial is already in standard form.

Answer 1

To write the polynomial \( 3w - w^6 + 0.4w^3 - 9.5 \) in standard form, we need to arrange the terms in descending order of their degree.

The individual terms are:
- \( -w^6 \) (degree 6)
- \( 0.4w^3 \) (degree 3)
- \( 3w \) (degree 1)
- \( -9.5 \) (degree 0)

Arranging these from the highest degree to the lowest, we get:

\[
-w^6 + 0.4w^3 + 3w - 9.5
\]

### Part 1
**Choice A is correct.** The standard form of the polynomial is:

\[
-w^6 + 0.4w^3 + 3w - 9.5
\]

### Degree and Leading Coefficient
- The **degree** of the polynomial is the highest exponent, which is 6.
- The **leading coefficient** is the coefficient of the term with the highest degree, which is \(-1\) in this case.

Thus:
- **Degree**: 6
- **Leading Coefficient**: -1