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Answer :
To determine the leading coefficient and the degree of the polynomial [tex]\(-x^4 + 18x + 23x^5 - 23\)[/tex], we'll follow these steps:
1. Rewrite the Polynomial in Standard Form:
A polynomial is typically written in descending order according to the powers of [tex]\(x\)[/tex]. So, let's arrange it properly:
[tex]\[
23x^5 - x^4 + 18x - 23
\][/tex]
2. Identify the Degree of the Polynomial:
The degree of a polynomial is the highest power of [tex]\(x\)[/tex] with a non-zero coefficient. In our polynomial [tex]\(23x^5 - x^4 + 18x - 23\)[/tex], the highest power of [tex]\(x\)[/tex] is [tex]\(5\)[/tex] (from the term [tex]\(23x^5\)[/tex]).
Therefore, the degree of the polynomial is [tex]\(5\)[/tex].
3. Determine the Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest power of [tex]\(x\)[/tex]. In our reordered polynomial, this term is [tex]\(23x^5\)[/tex]. Thus, the leading coefficient is [tex]\(23\)[/tex].
Therefore, the leading coefficient of the polynomial is [tex]\(23\)[/tex], and the degree is [tex]\(5\)[/tex].
1. Rewrite the Polynomial in Standard Form:
A polynomial is typically written in descending order according to the powers of [tex]\(x\)[/tex]. So, let's arrange it properly:
[tex]\[
23x^5 - x^4 + 18x - 23
\][/tex]
2. Identify the Degree of the Polynomial:
The degree of a polynomial is the highest power of [tex]\(x\)[/tex] with a non-zero coefficient. In our polynomial [tex]\(23x^5 - x^4 + 18x - 23\)[/tex], the highest power of [tex]\(x\)[/tex] is [tex]\(5\)[/tex] (from the term [tex]\(23x^5\)[/tex]).
Therefore, the degree of the polynomial is [tex]\(5\)[/tex].
3. Determine the Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest power of [tex]\(x\)[/tex]. In our reordered polynomial, this term is [tex]\(23x^5\)[/tex]. Thus, the leading coefficient is [tex]\(23\)[/tex].
Therefore, the leading coefficient of the polynomial is [tex]\(23\)[/tex], and the degree is [tex]\(5\)[/tex].
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