Question
Rewrite the following polynomial in standard form. \[ -\frac{x^{3}}{4}+10 x^{5}-5 \]
Ask by Washington Whittaker. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The standard form of the polynomial is \(10x^{5} - \frac{x^{3}}{4} - 5\).
Solution
To rewrite the polynomial \(-\frac{x^{3}}{4} + 10x^{5} - 5\) in standard form, arrange the terms in descending order of their exponents.
The standard form of a polynomial lists the terms starting with the highest power of \(x\) and ending with the constant term.
Here’s the polynomial reordered:
\[
10x^{5} - \frac{x^{3}}{4} - 5
\]
This places the \(x^5\) term first, followed by the \(x^3\) term, and finally the constant term.
**Standard Form:**
\[
10x^{5} - \frac{x^{3}}{4} - 5
\]
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Simplify this solution Beyond the Answer
To rewrite the polynomial in standard form, we need to arrange the terms in descending order of their degrees. The given polynomial is \[-\frac{x^{3}}{4} + 10 x^{5} - 5.\] Arranging the terms from the highest degree to the lowest, we get: \[10x^{5} - \frac{x^{3}}{4} - 5.\] So, the polynomial in standard form is \[10x^{5} - \frac{x^{3}}{4} - 5.\]
