Name: ______________________________________

Date: ______________________________________

**Classifying and Simplifying Polynomials**

Simplify each polynomial and write it in standard form. Then classify it based on its degree and number of terms.

1.
\[
\begin{array}{l}
8x - 2 + x^2 - 20x + 5 \\
8x - 20x = -12x \\
-2 + 5 = 3 \\
\text{Standard form: } x^2 - 12x + 3 \\
\text{Degree: } 2 \quad \text{Number of terms: } 3
\end{array}
\]

2.
\[
\begin{array}{l}
5x^2 - 9x^3 - 8x + x^2 \\
5x^2 + x^2 = 6x^2 \\
\text{Standard form: } -9x^3 + 6x^2 - 8x \\
\text{Degree: } 3 \quad \text{Number of terms: } 3
\end{array}
\]

3.
\[
x^5 - 24 - 5x^5 + 13
\]
\[
x^5 - 5x^5 = -4x^5 \\
-24 + 13 = -11 \\
\text{Standard form: } -4x^5 - 11 \\
\text{Degree: } 5 \quad \text{Number of terms: } 2
\]

4.
\[
-19x + 5 + 19x
\]
\[
-19x + 19x = 0 \\
\text{Standard form: } 5 \\
\text{Degree: } 0 \quad \text{Number of terms: } 1
\]

5.
\[
\begin{array}{l}
26x^4 - 9 + 3x - 17x^2 \\
\text{Standard form: } 26x^4 - 17x^2 + 3x - 9 \\
\text{Degree: } 4 \quad \text{Number of terms: } 4
\end{array}
\]

6.
\[
-13x^3 - 9x + 27x^3
\]
\[
-13x^3 + 27x^3 = 14x^3 \\
\text{Standard form: } 14x^3 - 9x \\
\text{Degree: } 3 \quad \text{Number of terms: } 2
\]

7.
\[
4x - 18 - 5x + 17
\]
\[
4x - 5x = -x \\
-18 + 17 = -1 \\
\text{Standard form: } -x - 1 \\
\text{Degree: } 1 \quad \text{Number of terms: } 2
\]

8.
\[
39x^3 + 18x - 1 + 5x^4
\]
\[
\text{Standard form: } 5x^4 + 39x^3 + 18x - 1 \\
\text{Degree: } 4 \quad \text{Number of terms: } 4
\]

9.
\[
-45 - \frac{1}{8}x + 30 + 10x + 15
\]
\[
10x - \frac{1}{8}x = \frac{79}{8}x \\
-45 + 30 + 15 = 0 \\
\text{Standard form: } \frac{79}{8}x \\
\text{Degree: } 1 \quad \text{Number of terms: } 1
\]

10.
\[
-x - 13 + 3x - 2x + 11x^2
\]
\[
-x + 3x - 2x = 0 \\
\text{Standard form: } 11x^2 - 13 \\
\text{Degree: } 2 \quad \text{Number of terms: } 2
\]

11.
\[
35x^3 + 12x^8 - 22x
\]
\[
\text{Standard form: } 12x^8 + 35x^3 - 22x \\
\text{Degree: } 8 \quad \text{Number of terms: } 3
\]