Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

In the polynomial function below, what is the leading coefficient?

[tex]\[ F(x)=\frac{1}{4} x^5+8x-5x^4-19 \][/tex]

A. [tex]\(-19\)[/tex]
B. [tex]\(\frac{1}{4}\)[/tex]
C. [tex]\(-5\)[/tex]
D. [tex]\(2\)[/tex]
E. [tex]\(8\)[/tex]

Sagot :

GinnyAnswer
To determine the leading coefficient of the polynomial [tex]\( F(x) = \frac{1}{4} x^5 + 8 x - 5 x^4 - 19 \)[/tex], follow these steps:

1. Identify the term with the highest degree: The degree of a term in a polynomial is the exponent of [tex]\( x \)[/tex]. In the provided polynomial, the terms and their respective degrees are as follows:
- [tex]\(\frac{1}{4} x^5\)[/tex] has a degree of 5.
- [tex]\(8x\)[/tex] has a degree of 1.
- [tex]\(-5 x^4\)[/tex] has a degree of 4.
- [tex]\(-19\)[/tex] is a constant term with a degree of 0 (since [tex]\( x^0 = 1 \)[/tex]).

2. Find the highest degree: From the identified terms, the term [tex]\(\frac{1}{4} x^5\)[/tex] has the highest degree, which is 5.

3. Determine the leading coefficient: The leading coefficient is the coefficient of the term with the highest degree. In this case, the term with the highest degree is [tex]\(\frac{1}{4} x^5\)[/tex], and its coefficient is [tex]\(\frac{1}{4}\)[/tex].

Thus, the leading coefficient of the polynomial [tex]\( F(x) = \frac{1}{4} x^5 + 8 x - 5 x^4 - 19 \)[/tex] is [tex]\(\frac{1}{4}\)[/tex].

Therefore, the correct answer is:
B. [tex]\(\frac{1}{4}\)[/tex].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.