Pregunta
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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The polynomial in standard form is \( x^{4} + \frac{1}{5}x^{3} - 1 \).
Solución
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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Simplifique esta solución 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: \[ x^4 + \frac{1}{5} x^{3} - 1 \]
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