To rewrite the polynomial in standard form, follow these steps:
1. Identify the given polynomial:
[tex]\[
-3x^5 - x - 4x^4 - \frac{1}{10} + 2x^3
\][/tex]
2. List the terms in the polynomial by their degree:
- The term with [tex]\( x^5 \)[/tex]: [tex]\(-3x^5\)[/tex]
- The term with [tex]\( x^4 \)[/tex]: [tex]\(-4x^4\)[/tex]
- The term with [tex]\( x^3 \)[/tex]: [tex]\(2x^3\)[/tex]
- The term with [tex]\( x \)[/tex]: [tex]\(-x\)[/tex]
- The constant term: [tex]\(-\frac{1}{10}\)[/tex]
3. Order the terms by the degree of [tex]\( x \)[/tex], from highest to lowest:
- Highest degree ([tex]\( x^5 \)[/tex]): [tex]\(-3x^5\)[/tex]
- Second highest degree ([tex]\( x^4 \)[/tex]): [tex]\(-4x^4\)[/tex]
- Next ([tex]\( x^3 \)[/tex]): [tex]\(2x^3\)[/tex]
- Next ([tex]\( x \)[/tex]): [tex]\(-x\)[/tex]
- Lowest degree (constant term): [tex]\(-\frac{1}{10}\)[/tex]
4. Combine the ordered terms into a single polynomial:
[tex]\[
-3x^5 - 4x^4 + 2x^3 - x - \frac{1}{10}
\][/tex]
5. Conclusion:
The polynomial in standard form is:
[tex]\[
-3x^5 - 4x^4 + 2x^3 - x - \frac{1}{10}
\][/tex]
Therefore, the answer is:
[tex]\[
-3x^5 - 4x^4 + 2x^3 - x - \frac{1}{10}
\][/tex]
