Let's complete the table by classifying each polynomial by its degree and number of terms.
1. For the polynomial [tex]\(2 x^2\)[/tex]:
- The highest power of [tex]\(x\)[/tex] is 2. The degree of this polynomial is quadratic.
- There is only one term in the polynomial. Therefore, it is a monomial.
2. For the polynomial [tex]\(-2\)[/tex]:
- There is no variable [tex]\(x\)[/tex] present in this polynomial. Hence, it is a constant polynomial.
- Since it is a single term, it is a monomial.
3. For the polynomial [tex]\(3x-9\)[/tex]:
- The highest power of [tex]\(x\)[/tex] is 1. The degree of this polynomial is linear.
- There are two terms present ([tex]\(3x\)[/tex] and [tex]\(-9\)[/tex]). Thus, it is a binomial.
Now, we can fill in the table accordingly:
\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{c}
Polynomial
\end{tabular} & \begin{tabular}{c}
Name Using \\
Degree
\end{tabular} & \begin{tabular}{c}
Name Using \\
Number of Terms
\end{tabular} \\
\hline [tex]$2 x^2$[/tex] & quadratic & monomial \\
\hline-2 & constant & monomial \\
\hline [tex]$3 x-9$[/tex] & linear & binomial \\
\hline
\end{tabular}
