Question
Determine the leading coefficient in the polynomial \( -4x^{4} + x^{2} - 6 \).
Ask by Hobbs Fernandez. in South Africa
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The leading coefficient is \(-4\).
Solution
The leading coefficient of a polynomial is the coefficient of the term with the highest degree (the highest power of \( x \)).
Given the polynomial:
\[
-4x^{4} + x^{2} - 6
\]
1. **Identify the highest power of \( x \):**
- The exponents of \( x \) are 4, 2, and 0 (for the constant term \(-6\)).
- The highest power is **4**.
2. **Determine the coefficient of the highest power term:**
- The term with \( x^4 \) is \(-4x^4\).
- The coefficient is **\(-4\)**.
**Answer:** \(-4\)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In the polynomial \( -4x^{4} + x^{2} - 6 \), the term with the highest degree is \( -4x^{4} \). Thus, the leading coefficient is \( -4 \). So, the leading coefficient in the polynomial \( -4x^{4} + x^{2} - 6 \) is \( -4 \).
