Answer :
To determine the leading coefficient and the degree of a polynomial, we need to look at its structure.
The polynomial given is [tex]\(23x^4 + 18x^3 - 7 + 6x\)[/tex].
1. Identify the Degree of the Polynomial:
- The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] that appears in the polynomial with a non-zero coefficient.
- In this polynomial, the highest power of [tex]\(x\)[/tex] is [tex]\(x^4\)[/tex].
Therefore, the degree of the polynomial is [tex]\(4\)[/tex].
2. Find the Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest power of [tex]\(x\)[/tex].
- The term with the highest power here is [tex]\(23x^4\)[/tex], so the coefficient is [tex]\(23\)[/tex].
So, the leading coefficient is [tex]\(23\)[/tex], and the degree of the polynomial is [tex]\(4\)[/tex].
The polynomial given is [tex]\(23x^4 + 18x^3 - 7 + 6x\)[/tex].
1. Identify the Degree of the Polynomial:
- The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] that appears in the polynomial with a non-zero coefficient.
- In this polynomial, the highest power of [tex]\(x\)[/tex] is [tex]\(x^4\)[/tex].
Therefore, the degree of the polynomial is [tex]\(4\)[/tex].
2. Find the Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest power of [tex]\(x\)[/tex].
- The term with the highest power here is [tex]\(23x^4\)[/tex], so the coefficient is [tex]\(23\)[/tex].
So, the leading coefficient is [tex]\(23\)[/tex], and the degree of the polynomial is [tex]\(4\)[/tex].
