We appreciate your visit to What are the degree and leading coefficient of the polynomial tex 4x 23x 4 2 12x 5 tex Degree tex square tex Leading coefficient tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine the degree and the leading coefficient of the polynomial [tex]\(4x + 23x^4 + 2 - 12x^5\)[/tex], follow these steps:
1. Identify the Terms: Write down the terms of the polynomial and their respective powers and coefficients:
- [tex]\(4x\)[/tex] has a degree of 1 and a coefficient of 4.
- [tex]\(23x^4\)[/tex] has a degree of 4 and a coefficient of 23.
- [tex]\(2\)[/tex] is a constant term and can be seen as [tex]\(2x^0\)[/tex], which has a degree of 0 and a coefficient of 2.
- [tex]\(-12x^5\)[/tex] has a degree of 5 and a coefficient of -12.
2. Determine the Degree: The degree of the polynomial is the highest power of [tex]\(x\)[/tex] present in any term, which in this case is 5 from the term [tex]\(-12x^5\)[/tex].
3. Identify the Leading Coefficient: The leading coefficient is the coefficient of the term with the highest degree. Since [tex]\(-12x^5\)[/tex] is the term with the highest degree, its coefficient, [tex]\(-12\)[/tex], is the leading coefficient.
So, for the polynomial [tex]\(4x + 23x^4 + 2 - 12x^5\)[/tex]:
- The degree is [tex]\(5\)[/tex].
- The leading coefficient is [tex]\(-12\)[/tex].
1. Identify the Terms: Write down the terms of the polynomial and their respective powers and coefficients:
- [tex]\(4x\)[/tex] has a degree of 1 and a coefficient of 4.
- [tex]\(23x^4\)[/tex] has a degree of 4 and a coefficient of 23.
- [tex]\(2\)[/tex] is a constant term and can be seen as [tex]\(2x^0\)[/tex], which has a degree of 0 and a coefficient of 2.
- [tex]\(-12x^5\)[/tex] has a degree of 5 and a coefficient of -12.
2. Determine the Degree: The degree of the polynomial is the highest power of [tex]\(x\)[/tex] present in any term, which in this case is 5 from the term [tex]\(-12x^5\)[/tex].
3. Identify the Leading Coefficient: The leading coefficient is the coefficient of the term with the highest degree. Since [tex]\(-12x^5\)[/tex] is the term with the highest degree, its coefficient, [tex]\(-12\)[/tex], is the leading coefficient.
So, for the polynomial [tex]\(4x + 23x^4 + 2 - 12x^5\)[/tex]:
- The degree is [tex]\(5\)[/tex].
- The leading coefficient is [tex]\(-12\)[/tex].
Thanks for taking the time to read What are the degree and leading coefficient of the polynomial tex 4x 23x 4 2 12x 5 tex Degree tex square tex Leading coefficient tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
