Let's consider the algebraic expression [tex]\(\sqrt{13} x^{19} + 19.8 x^{15} + \pi x^{10} + \frac{1}{5}\)[/tex]. We'll solve for the following:
1. The degree of the polynomial
2. The constant term
3. The leading coefficient
4. The leading term
### 1. Degree of the Polynomial
The degree of a polynomial is determined by the highest power of [tex]\(x\)[/tex] in the expression. In this polynomial, the highest power of [tex]\(x\)[/tex] is 19 from the term [tex]\(\sqrt{13} x^{19}\)[/tex].
Thus, the degree of the polynomial is:
[tex]\[
\boxed{19}
\][/tex]
### 2. Constant Term
The constant term in a polynomial is the term that does not contain any [tex]\(x\)[/tex]. Here, the term [tex]\(\frac{1}{5}\)[/tex] is the only term without [tex]\(x\)[/tex].
Thus, the constant term is:
[tex]\[
\boxed{\frac{1}{5}}
\][/tex]
### 3. Leading Coefficient
The leading coefficient is the coefficient of the term with the highest degree. The highest degree is 19, and the term with this degree is [tex]\(\sqrt{13} x^{19}\)[/tex]. The coefficient of this term is [tex]\(\sqrt{13}\)[/tex].
Thus, the leading coefficient is:
[tex]\[
\boxed{\sqrt{13}}
\][/tex]
### 4. Leading Term
The leading term is the term with the highest degree, which is [tex]\(\sqrt{13} x^{19}\)[/tex].
Thus, the leading term is:
[tex]\[
\boxed{\sqrt{13} x^{19}}
\][/tex]
To summarize:
1. The degree of the polynomial is [tex]\(19\)[/tex].
2. The constant term is [tex]\(\frac{1}{5}\)[/tex].
3. The leading coefficient is [tex]\(\sqrt{13}\)[/tex].
4. The leading term is [tex]\(\sqrt{13} x^{19}\)[/tex].
