Answer :
To determine the leading coefficient of a polynomial, you need to identify the term with the highest degree, and then find the coefficient of that term.
Let's analyze the polynomial function:
[tex]\[ F(x) = \frac{1}{3} x^3 + 8 x^4 - 5 x - 19 x^2 \][/tex]
Step-by-step solution:
1. Identify the Degree of Each Term:
- [tex]\(\frac{1}{3} x^3\)[/tex] has a degree of 3.
- [tex]\(8 x^4\)[/tex] has a degree of 4.
- [tex]\(-5 x\)[/tex] has a degree of 1.
- [tex]\(-19 x^2\)[/tex] has a degree of 2.
2. Identify the Term with the Highest Degree:
Looking at the degrees we calculated, the highest degree is 4, which is for the term [tex]\(8 x^4\)[/tex].
3. Find the Coefficient of the Highest Degree Term:
The coefficient of the term [tex]\(8 x^4\)[/tex] is 8.
Therefore, the leading coefficient of the polynomial function is 8.
So, the correct answer is A. 8.
Let's analyze the polynomial function:
[tex]\[ F(x) = \frac{1}{3} x^3 + 8 x^4 - 5 x - 19 x^2 \][/tex]
Step-by-step solution:
1. Identify the Degree of Each Term:
- [tex]\(\frac{1}{3} x^3\)[/tex] has a degree of 3.
- [tex]\(8 x^4\)[/tex] has a degree of 4.
- [tex]\(-5 x\)[/tex] has a degree of 1.
- [tex]\(-19 x^2\)[/tex] has a degree of 2.
2. Identify the Term with the Highest Degree:
Looking at the degrees we calculated, the highest degree is 4, which is for the term [tex]\(8 x^4\)[/tex].
3. Find the Coefficient of the Highest Degree Term:
The coefficient of the term [tex]\(8 x^4\)[/tex] is 8.
Therefore, the leading coefficient of the polynomial function is 8.
So, the correct answer is A. 8.
