Question
Rewrite the following polynomial in standard form. \[ 10 x-\frac{x^{4}}{5}-6 \]
Ask by Mcguire Powers. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The polynomial in standard form is \(-\frac{1}{5}x^{4} + 10x - 6\).
Solution
The polynomial \( 10x - \frac{x^{4}}{5} - 6 \) can be rewritten in standard form by arranging the terms in descending order of the degree of \( x \).
Here’s the step-by-step process:
1. **Identify the degrees of each term:**
- \(-\frac{x^4}{5}\) has degree 4.
- \(10x\) has degree 1.
- \(-6\) is a constant term with degree 0.
2. **Arrange the terms in descending order:**
- Start with the highest degree term: \(-\frac{x^4}{5}\).
- Follow with the next highest degree: \(10x\).
- End with the constant term: \(-6\).
So, the polynomial in standard form is:
\[
-\frac{1}{5}x^{4} + 10x - 6
\]
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Simplify this solution Bonus Knowledge
To rewrite the polynomial in standard form, we need to arrange the terms in descending order according to the power of \( x \). First, let's simplify the term \(-\frac{x^4}{5}\) and then combine all the terms together: \[ -\frac{x^4}{5} + 10x - 6 \] Now, express it in standard form: \[ -\frac{1}{5}x^4 + 10x - 6 \] So, the polynomial in standard form is: \[ -\frac{1}{5}x^4 + 10x - 6 \]
