Question
Question Rewrite the following polynomial in standard form. \[ \frac{1}{5} x^{3}-1+x^{4} \] Answer Attempt 1 out of 2 Answer:
Ask by Wyatt Daniel. in the United States
Jan 27,2025
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Tutor-Verified Answer
Answer
The polynomial in standard form is \( x^{4} + \frac{1}{5}x^{3} - 1 \).
Solution
To rewrite the polynomial \(\frac{1}{5}x^{3} - 1 + x^{4}\) in standard form, arrange the terms in descending order of their exponents:
1. **Identify the degrees of each term:**
- \(x^{4}\) has a degree of 4.
- \(\frac{1}{5}x^{3}\) has a degree of 3.
- \(-1\) is a constant term with a degree of 0.
2. **Arrange the terms from highest to lowest degree:**
\[ x^{4} + \frac{1}{5}x^{3} - 1 \]
**Standard Form:**
\[ x^{4} + \frac{1}{5}x^{3} - 1 \]
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Simplify this solution Beyond the Answer
To rewrite the polynomial in standard form, we need to reorder the terms based on the degree of each term, placing the highest degree term first. Starting with the original expression: \( \frac{1}{5} x^{3}-1+x^{4} \), we identify the degrees: \( x^4 \) (degree 4), \( \frac{1}{5} x^{3} \) (degree 3), and \(-1\) (degree 0). Now, we can write it in standard form as: \[ x^4 + \frac{1}{5} x^{3} - 1 \]
