Let's classify each polynomial based on its degree and the number of terms:
1. [tex]\(2 x^2\)[/tex]:
- Degree: The highest power of [tex]\(x\)[/tex] is 2. Therefore, it is a quadratic polynomial.
- Number of Terms: There is only one term. Therefore, it is a monomial.
2. -2:
- Degree: There is no [tex]\(x\)[/tex] term. Therefore, it is a constant polynomial.
- Number of Terms: There is only one term. Therefore, it is a monomial.
3. [tex]\(3 x - 9\)[/tex]:
- Degree: The highest power of [tex]\(x\)[/tex] is 1. Therefore, it is a linear polynomial.
- Number of Terms: There are two terms. Therefore, it is a binomial.
4. [tex]\(-3 x^2 - 6 x + 9\)[/tex]:
- Degree: The highest power of [tex]\(x\)[/tex] is 2. Therefore, it is a quadratic polynomial.
- Number of Terms: There are three terms. Therefore, it is a trinomial.
Based on this classification, the completed table is:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline \text{Polynominal} & \begin{tabular}{c}
\text{Name Using} \\
\text{Degree}
\end{tabular} & \begin{tabular}{c}
\text{Name Using} \\
\text{Number of Terms}
\end{tabular} \\
\hline
$2 x^2$ & quadratic & monomial \\
\hline
-2 & constant & monomial \\
\hline
$3 x-9$ & linear & binomial \\
\hline
$-3 x^2-6 x+9$ & quadratic & trinomial \\
\hline
\end{tabular}
\][/tex]
