Thank you for visiting Classifying Simplifying Polynomials Degree and Number of Terms 1 Simplify the expression 8x 2 x 2 20x 5 Combine like terms 8x 20x 2 5. 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!
Answer :
Sure! Let's go through each polynomial and simplify by combining like terms:
1. Polynomial: [tex]\(8x - 2 + x^2 - 20x + 5\)[/tex]
- Combine like terms:
- [tex]\(8x - 20x = -12x\)[/tex]
- [tex]\(-2 + 5 = 3\)[/tex]
- The simplified form is:
[tex]\[x^2 - 12x + 3\][/tex]
2. Polynomial: [tex]\(5x^2 - 4x^3 - 8x + x^2 - 8x\)[/tex]
- Combine like terms:
- [tex]\(5x^2 + x^2 = 6x^2\)[/tex]
- [tex]\(-8x - 8x = -16x\)[/tex]
- The simplified form is:
[tex]\[-4x^3 + 6x^2 - 16x\][/tex]
3. Polynomial: [tex]\(x^6 - 24 - 5x^5 + 13\)[/tex]
- No like terms to combine:
- The expression simplifies to:
[tex]\[x^6 - 5x^5 - 11\][/tex]
5. Polynomial: [tex]\(26x^4 - 9 + 3x - 17x^2\)[/tex]
- No like terms between the terms:
- The simplified form is:
[tex]\[26x^4 - 17x^2 + 3x - 9\][/tex]
6. Additional Reduction: [tex]\(713x^3 - 9x + 27x^3\)[/tex]
- Combine like terms:
- [tex]\(713x^3 + 27x^3 = 740x^3\)[/tex]
- The simplified form is:
[tex]\[740x^3 - 9x\][/tex]
8. Polynomial: [tex]\(4x - 18 - 5x + 17\)[/tex]
- Combine like terms:
- [tex]\(4x - 5x = -x\)[/tex]
- [tex]\(-18 + 17 = -1\)[/tex]
- The simplified form is:
[tex]\[-x - 1\][/tex]
9. Polynomial: [tex]\(39x^3 + 18x - 1 + 5x^4 - x^2\)[/tex]
- No further similar terms, order by degree:
- The simplified form is:
[tex]\[5x^4 + 39x^3 - x^2 + 18x - 1\][/tex]
10. Polynomial: [tex]\(-45 - \frac{1}{8}x + 30 + 10x + 15\)[/tex]
- Combine like terms:
- [tex]\(-\frac{1}{8}x + 10x = \frac{79}{8}x\)[/tex]
- [tex]\(-45 + 30 + 15 = 0\)[/tex]
- The simplified form is:
[tex]\[\frac{79}{8}x\][/tex]
II. Polynomial: [tex]\(-x - 13 + 3x - 2x + 11x^2\)[/tex]
- Combine like terms:
- [tex]\(-x + 3x - 2x = 0\)[/tex]
- The expression with no x terms is:
[tex]\[11x^2 - 13\][/tex]
This completes the simplification of each polynomial, displaying them with like terms combined.
1. Polynomial: [tex]\(8x - 2 + x^2 - 20x + 5\)[/tex]
- Combine like terms:
- [tex]\(8x - 20x = -12x\)[/tex]
- [tex]\(-2 + 5 = 3\)[/tex]
- The simplified form is:
[tex]\[x^2 - 12x + 3\][/tex]
2. Polynomial: [tex]\(5x^2 - 4x^3 - 8x + x^2 - 8x\)[/tex]
- Combine like terms:
- [tex]\(5x^2 + x^2 = 6x^2\)[/tex]
- [tex]\(-8x - 8x = -16x\)[/tex]
- The simplified form is:
[tex]\[-4x^3 + 6x^2 - 16x\][/tex]
3. Polynomial: [tex]\(x^6 - 24 - 5x^5 + 13\)[/tex]
- No like terms to combine:
- The expression simplifies to:
[tex]\[x^6 - 5x^5 - 11\][/tex]
5. Polynomial: [tex]\(26x^4 - 9 + 3x - 17x^2\)[/tex]
- No like terms between the terms:
- The simplified form is:
[tex]\[26x^4 - 17x^2 + 3x - 9\][/tex]
6. Additional Reduction: [tex]\(713x^3 - 9x + 27x^3\)[/tex]
- Combine like terms:
- [tex]\(713x^3 + 27x^3 = 740x^3\)[/tex]
- The simplified form is:
[tex]\[740x^3 - 9x\][/tex]
8. Polynomial: [tex]\(4x - 18 - 5x + 17\)[/tex]
- Combine like terms:
- [tex]\(4x - 5x = -x\)[/tex]
- [tex]\(-18 + 17 = -1\)[/tex]
- The simplified form is:
[tex]\[-x - 1\][/tex]
9. Polynomial: [tex]\(39x^3 + 18x - 1 + 5x^4 - x^2\)[/tex]
- No further similar terms, order by degree:
- The simplified form is:
[tex]\[5x^4 + 39x^3 - x^2 + 18x - 1\][/tex]
10. Polynomial: [tex]\(-45 - \frac{1}{8}x + 30 + 10x + 15\)[/tex]
- Combine like terms:
- [tex]\(-\frac{1}{8}x + 10x = \frac{79}{8}x\)[/tex]
- [tex]\(-45 + 30 + 15 = 0\)[/tex]
- The simplified form is:
[tex]\[\frac{79}{8}x\][/tex]
II. Polynomial: [tex]\(-x - 13 + 3x - 2x + 11x^2\)[/tex]
- Combine like terms:
- [tex]\(-x + 3x - 2x = 0\)[/tex]
- The expression with no x terms is:
[tex]\[11x^2 - 13\][/tex]
This completes the simplification of each polynomial, displaying them with like terms combined.
Thank you for reading the article Classifying Simplifying Polynomials Degree and Number of Terms 1 Simplify the expression 8x 2 x 2 20x 5 Combine like terms 8x 20x 2 5. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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