To classify each polynomial expression based on its degree and the number of terms, we'll follow these steps:
1. Identify the degree of each polynomial:
- The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] in the polynomial's terms.
- Terms without an [tex]\( x \)[/tex] (constant terms) have a degree of 0.
2. Count the number of terms in each polynomial:
- A polynomial with one term is called a monomial.
- A polynomial with two terms is called a binomial.
- A polynomial with three terms is called a trinomial.
Let's classify each given polynomial:
1. Polynomial: [tex]\( 5x \)[/tex]
- Degree: The highest exponent of [tex]\( x \)[/tex] is 1. This makes it a linear polynomial.
- Number of Terms: There is 1 term, so it is a monomial.
2. Polynomial: [tex]\( -7 \)[/tex]
- Degree: As there is no [tex]\( x \)[/tex], the exponent is 0. This makes it a constant polynomial.
- Number of Terms: There is 1 term, so it is a monomial.
3. Polynomial: [tex]\( x^2 + 4 \)[/tex]
- Degree: The highest exponent of [tex]\( x \)[/tex] is 2. This makes it a quadratic polynomial.
- Number of Terms: There are 2 terms, so it is a binomial.
4. Polynomial: [tex]\( x^2 - 3x + 11 \)[/tex]
- Degree: The highest exponent of [tex]\( x \)[/tex] is 2. This makes it a quadratic polynomial.
- Number of Terms: There are 3 terms, so it is a trinomial.
5. Polynomial: [tex]\( 2x - 9 \)[/tex]
- Degree: The highest exponent of [tex]\( x \)[/tex] is 1. This makes it a linear polynomial.
- Number of Terms: There are 2 terms, so it is a binomial.
Now, let's fill the table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
Polynomial & Name Using Degree & Name Using Number of Terms \\
\hline
$5x$ & linear & monomial \\
\hline
$-7$ & constant & monomial \\
\hline
$x^2 + 4$ & quadratic & binomial \\
\hline
$x^2 - 3x + 11$ & quadratic & trinomial \\
\hline
$2x - 9$ & linear & binomial \\
\hline
\end{tabular}
\][/tex]
This classification gives a clear understanding of the degree and number of terms for each polynomial.
