Question

what is the leading coefficient of the polynomial $f(x)$ defined below? $f(x) = 8x - 8x^3 - x^4 + 6$

Explanation:

Step1: Recall the definition of leading coefficient

The leading coefficient of a polynomial is the coefficient of the term with the highest degree (exponent).

Step2: Identify the term with the highest degree in the polynomial \( f(x) = 8x - 8x^3 - x^4 + 6 \)

First, find the degrees of each term:

• For the term \( 8x \), the degree is \( 1 \) (since the exponent of \( x \) is \( 1 \)).
• For the term \( -8x^3 \), the degree is \( 3 \).
• For the term \( -x^4 \), the degree is \( 4 \).
• For the constant term \( 6 \), the degree is \( 0 \).

The highest degree among these terms is \( 4 \), and the term with degree \( 4 \) is \( -x^4 \).

Step3: Determine the leading coefficient

The coefficient of the term \( -x^4 \) is \( -1 \) (because \( -x^4 = -1 \cdot x^4 \)).

Answer:

\(-1\)