Sure! Let's determine the degree of each polynomial expression step-by-step.
### Explanation:
1. Degrees of a Polynomial:
- The degree of a polynomial is the highest power of the variable in the expression.
- Constant terms (numbers without variables) have a degree of 0.
- The degree of a zero polynomial (if any term only multiplies 0) is usually not defined, but is sometimes considered to be -∞ for comparative purposes.
### Examining Each Polynomial Expression:
Let's look at each polynomial one by one to find the degree.
1. Expression: [tex]\( x - 9 \)[/tex]
- The variable [tex]\( x \)[/tex] is raised to the power of 1.
- Therefore, the degree is 1.
2. Expression: [tex]\( -4x^2 - 6x + 9 \)[/tex]
- The highest power of the variable [tex]\( x \)[/tex] is 2 (from the term [tex]\( -4x^2 \)[/tex]).
- Therefore, the degree is 2.
3. Expression: [tex]\( x^2 - 2x + 9 \)[/tex]
- The highest power of the variable [tex]\( x \)[/tex] is 2 (from the term [tex]\( x^2 \)[/tex]).
- Therefore, the degree is 2.
4. Expression: [tex]\( -3 \)[/tex]
- This is a constant term, so it does not have any variable.
- Therefore, the degree is 0.
5. Expression: [tex]\( 3x - 2 \)[/tex]
- The highest power of the variable [tex]\( x \)[/tex] is 1 (from the term [tex]\( 3x \)[/tex]).
- Therefore, the degree is 1.
6. Expression: [tex]\( 6x + 2 \)[/tex]
- The highest power of the variable [tex]\( x \)[/tex] is 1 (from the term [tex]\( 6x \)[/tex]).
- Therefore, the degree is 1.
7. Expression: [tex]\( 5 \)[/tex]
- This is a constant term, so it does not have any variable.
- Therefore, the degree is 0.
### Summary of Degrees:
Let's summarize the degrees:
[tex]\[
\begin{array}{c|c}
\text{Polynomial Expression} & \text{Degree} \\
\hline
x-9 & 1 \\
-4 x^2-6 x+9 & 2 \\
x^2-2 x+9 & 2 \\
-3 & 0 \\
3 x-2 & 1 \\
6 x+2 & 1 \\
5 & 0 \\
\end{array}
\][/tex]
So, the degrees of the polynomial expressions in your list are:
[tex]\[
\begin{array}{c}
1 \\
2 \\
2 \\
0 \\
1 \\
1 \\
0 \\
\end{array}
\][/tex]
