Answer :
To find the leading coefficient of a polynomial function, you need to identify the term with the highest power of [tex]\(x\)[/tex]. The coefficient of that term is the leading coefficient.
Let's break down the polynomial function [tex]\( F(x) = \frac{1}{3} x^3 + 8 x^4 - 5 x - 19 x^2 \)[/tex]:
1. Identify each term's degree:
- [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. Find the term with the highest degree:
- Out of the terms [tex]\(\frac{1}{3} x^3\)[/tex], [tex]\(8 x^4\)[/tex], [tex]\(-5 x\)[/tex], and [tex]\(-19 x^2\)[/tex], the term [tex]\(8 x^4\)[/tex] has the highest degree, which is 4.
3. Determine the leading coefficient:
- 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 B. 8.
Let's break down the polynomial function [tex]\( F(x) = \frac{1}{3} x^3 + 8 x^4 - 5 x - 19 x^2 \)[/tex]:
1. Identify each term's degree:
- [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. Find the term with the highest degree:
- Out of the terms [tex]\(\frac{1}{3} x^3\)[/tex], [tex]\(8 x^4\)[/tex], [tex]\(-5 x\)[/tex], and [tex]\(-19 x^2\)[/tex], the term [tex]\(8 x^4\)[/tex] has the highest degree, which is 4.
3. Determine the leading coefficient:
- 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 B. 8.
