Let's classify each polynomial both by its degree and by the number of terms. Here is the classification:
1. Polynomial [tex]\(\frac{7}{4}x + 3\)[/tex]
- Degree Classification: This is a linear polynomial because the highest degree of [tex]\(x\)[/tex] is 1.
- Number of Terms Classification: This is a binomial because it has exactly two terms.
2. Polynomial [tex]\(5.2x^2 - 4x + 2.5\)[/tex]
- Degree Classification: This is a quadratic polynomial because the highest degree of [tex]\(x\)[/tex] is 2.
- Number of Terms Classification: This is a trinomial because it has three terms.
3. Polynomial [tex]\(\frac{3}{5}\)[/tex]
- Degree Classification: This is a constant polynomial because it does not have any [tex]\(x\)[/tex] term.
- Number of Terms Classification: This is a monomial because it has exactly one term.
4. Polynomial [tex]\(0.75x^2\)[/tex]
- Degree Classification: This is a quadratic polynomial because the highest degree of [tex]\(x\)[/tex] is 2.
- Number of Terms Classification: This is a monomial because it has exactly one term.
Now, placing the classifications into the table:
\begin{tabular}{|c|c|c|}
\hline
Polynomial & \begin{tabular}{c}
Name Using \\
Degree
\end{tabular} & \begin{tabular}{c}
Name Using \\
Number of Terms
\end{tabular} \\
\hline
[tex]$\frac{7}{4}x + 3$[/tex] & linear & binomial \\
\hline
[tex]$5.2x^2 - 4x + 2.5$[/tex] & quadratic & trinomial \\
\hline
[tex]$\frac{3}{5}$[/tex] & constant & monomial \\
\hline
[tex]$0.75x^2$[/tex] & quadratic & monomial \\
\hline
\end{tabular}
This table classifies each polynomial correctly based on both its degree and the number of terms.
