High School

Thank you for visiting 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. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

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

Answer :

Sure, let's go through each polynomial step by step to simplify and classify them. Remember, we'll first simplify the polynomials, arranging them in descending order of their powers, and then classify each based on its degree (highest power of x) and the number of terms.

1. Polynomial: [tex]\(8x - 2 + x^2 - 20x + 5\)[/tex]
- Combine like terms: [tex]\(x^2 + (8x - 20x) + (-2 + 5)\)[/tex]
- Simplified form: [tex]\(x^2 - 12x + 3\)[/tex]
- Degree: 2 (the highest power is [tex]\(x^2\)[/tex])
- Number of terms: 3

2. Polynomial: [tex]\(5x^2 - 9x^3 - 8x + x^2\)[/tex]
- Combine like terms: [tex]\((-9x^3) + (5x^2 + x^2) - 8x\)[/tex]
- Simplified form: [tex]\(-9x^3 + 6x^2 - 8x\)[/tex]
- Degree: 3 (the highest power is [tex]\(x^3\)[/tex])
- Number of terms: 3

3. Polynomial: [tex]\(x^5 - 24 - 5x^5 + 13\)[/tex]
- Combine like terms: [tex]\((x^5 - 5x^5) + (-24 + 13)\)[/tex]
- Simplified form: [tex]\(-4x^5 - 11\)[/tex]
- Degree: 5 (the highest power is [tex]\(x^5\)[/tex])
- Number of terms: 2

4. Polynomial: [tex]\(-19x + 19x\)[/tex]
- Combine like terms: [tex]\(-19x + 19x = 0\)[/tex]
- Degree: 0 (constant term, no x)
- Number of terms: 0

5. Polynomial: [tex]\(26x^4 - 9 + 3x - 17x^2\)[/tex]
- No like terms to combine; reorder: [tex]\(26x^4 - 17x^2 + 3x - 9\)[/tex]
- Degree: 4 (the highest power is [tex]\(x^4\)[/tex])
- Number of terms: 4

7. Polynomial: [tex]\(-13x^3 - 9x + 27x^3\)[/tex]
- Combine like terms: [tex]\((-13x^3 + 27x^3) - 9x\)[/tex]
- Simplified form: [tex]\(14x^3 - 9x\)[/tex]
- Degree: 3 (the highest power is [tex]\(x^3\)[/tex])
- Number of terms: 2

8. Polynomial: [tex]\(4x - 18 - 5x + 17\)[/tex]
- Combine like terms: [tex]\((4x - 5x) + (-18 + 17)\)[/tex]
- Simplified form: [tex]\(-x - 1\)[/tex]
- Degree: 1 (the highest power is [tex]\(x\)[/tex])
- Number of terms: 2

9. Polynomial: [tex]\(39x^3 + 18x - 1 + 5x^4\)[/tex]
- Reorder in descending order: [tex]\(5x^4 + 39x^3 + 18x - 1\)[/tex]
- Degree: 4 (the highest power is [tex]\(x^4\)[/tex])
- Number of terms: 4

10. Polynomial: [tex]\(-45 - \frac{1}{8}x + 30 + 10x + 15\)[/tex]
- Combine like terms: [tex]\((10x - \frac{1}{8}x) + (-45 + 30 + 15)\)[/tex]
- Simplified form: [tex]\(\frac{79}{8}x + 0\)[/tex]
- Degree: 1 (the highest power is [tex]\(x\)[/tex])
- Number of terms: 1

11. Polynomial: [tex]\(-x - 13 + 3x - 2x + 11x^2\)[/tex]
- Combine like terms: [tex]\(11x^2 + (-x + 3x - 2x) - 13\)[/tex]
- Simplified form: [tex]\(11x^2 - 13\)[/tex]
- Degree: 2 (the highest power is [tex]\(x^2\)[/tex])
- Number of terms: 2

12. Polynomial: [tex]\(35x^3 + 12x^8 - 22x\)[/tex]
- Reorder to standard form: [tex]\(12x^8 + 35x^3 - 22x\)[/tex]
- Degree: 8 (the highest power is [tex]\(x^8\)[/tex])
- Number of terms: 3

I hope this clear explanation helps! Let me know if you have any questions.

Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions