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Answer :
Sure! Let's break down the process of finding the leading coefficient and the degree of the polynomial expression:
The polynomial given is:
[tex]\[
-5x - 9 - 8x^4 + 23x^8
\][/tex]
Step 1: Identify the Degree of the Polynomial
The degree of a polynomial is determined by the highest power of the variable [tex]\(x\)[/tex] present in the expression. So, let's look at the powers of [tex]\(x\)[/tex] in each term:
- The term [tex]\(-5x\)[/tex] has a power of 1.
- The constant term [tex]\(-9\)[/tex] can be thought of as [tex]\(x^0\)[/tex], which has a power of 0.
- The term [tex]\(-8x^4\)[/tex] has a power of 4.
- The term [tex]\(23x^8\)[/tex] has a power of 8.
The highest power among these is 8. Therefore, the degree of the polynomial is 8.
Step 2: Identify the Leading Coefficient
The leading coefficient is the coefficient of the term with the highest degree. From our expression, the term with the highest degree is [tex]\(23x^8\)[/tex].
The coefficient of this term is 23. Hence, the leading coefficient is 23.
So, the leading coefficient is 23, and the degree of the polynomial is 8.
The polynomial given is:
[tex]\[
-5x - 9 - 8x^4 + 23x^8
\][/tex]
Step 1: Identify the Degree of the Polynomial
The degree of a polynomial is determined by the highest power of the variable [tex]\(x\)[/tex] present in the expression. So, let's look at the powers of [tex]\(x\)[/tex] in each term:
- The term [tex]\(-5x\)[/tex] has a power of 1.
- The constant term [tex]\(-9\)[/tex] can be thought of as [tex]\(x^0\)[/tex], which has a power of 0.
- The term [tex]\(-8x^4\)[/tex] has a power of 4.
- The term [tex]\(23x^8\)[/tex] has a power of 8.
The highest power among these is 8. Therefore, the degree of the polynomial is 8.
Step 2: Identify the Leading Coefficient
The leading coefficient is the coefficient of the term with the highest degree. From our expression, the term with the highest degree is [tex]\(23x^8\)[/tex].
The coefficient of this term is 23. Hence, the leading coefficient is 23.
So, the leading coefficient is 23, and the degree of the polynomial is 8.
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