Thank you for visiting Simplifying Polynomials Degree and Number of Terms1 Simplify tex 8x 2 x 2 20x 5 tex tex begin align 8x 20x 2 5 x 2. 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 simplify each polynomial step by step:
1. Simplify: [tex]\(8x - 2 + x^2 - 20x + 5\)[/tex]:
- Combine the like terms:
- [tex]\(8x - 20x = -12x\)[/tex]
- [tex]\(-2 + 5 = 3\)[/tex]
- So, the simplified form is: [tex]\(x^2 - 12x + 3\)[/tex]
2. Simplify: [tex]\(5x^2 - 9x^3 - 8x + x^2\)[/tex]:
- Combine the like terms:
- [tex]\(5x^2 + x^2 = 6x^2\)[/tex]
- So, the simplified form is: [tex]\(-9x^3 + 6x^2 - 8x\)[/tex]
3. Simplify: [tex]\(x^5 - 24 - 5x^5 + 13\)[/tex]:
- Combine the like terms:
- [tex]\(x^5 - 5x^5 = -4x^5\)[/tex]
- [tex]\(-24 + 13 = -11\)[/tex]
- So, the simplified form is: [tex]\(-4x^5 - 11\)[/tex]
4. Simplify: [tex]\(-19x + 5 + 19x\)[/tex]:
- Combine the like terms:
- [tex]\(-19x + 19x = 0\)[/tex]
- The constant term remains [tex]\(+5\)[/tex]
- So, the simplified form is: [tex]\(5\)[/tex]
5. Simplify: [tex]\(26x^4 - 9 + 3x - 17x^2\)[/tex]:
- There are no like terms to combine.
- So, the simplified form is: [tex]\(26x^4 - 17x^2 + 3x - 9\)[/tex]
6. Simplify: [tex]\(7x - 19 - 6x - 24 + 13x^2\)[/tex]:
- Combine the like terms:
- [tex]\(7x - 6x = x\)[/tex]
- [tex]\(-19 - 24 = -43\)[/tex]
- So, the simplified form is: [tex]\(13x^2 + x - 43\)[/tex]
7. Simplify: [tex]\(-13x^3 - 9x + 27x^3\)[/tex]:
- Combine the like terms:
- [tex]\(-13x^3 + 27x^3 = 14x^3\)[/tex]
- So, the simplified form is: [tex]\(14x^3 - 9x\)[/tex]
8. Simplify: [tex]\(4x - 18 - 5x + 17\)[/tex]:
- Combine the like terms:
- [tex]\(4x - 5x = -x\)[/tex]
- [tex]\(-18 + 17 = -1\)[/tex]
- So, the simplified form is: [tex]\(-x - 1\)[/tex]
9. Simplify: [tex]\(39x^3 + 18x - 1 + 5x^4 - x^2 - x - 1\)[/tex]:
- Combine the like terms:
- [tex]\(18x - x = 17x\)[/tex]
- [tex]\(-1 - 1 = -2\)[/tex]
- So, the simplified form is: [tex]\(5x^4 + 39x^3 - x^2 + 17x - 2\)[/tex]
These are the simplified forms of the given polynomials. If you have any more questions or need further clarification, feel free to ask!
1. Simplify: [tex]\(8x - 2 + x^2 - 20x + 5\)[/tex]:
- Combine the like terms:
- [tex]\(8x - 20x = -12x\)[/tex]
- [tex]\(-2 + 5 = 3\)[/tex]
- So, the simplified form is: [tex]\(x^2 - 12x + 3\)[/tex]
2. Simplify: [tex]\(5x^2 - 9x^3 - 8x + x^2\)[/tex]:
- Combine the like terms:
- [tex]\(5x^2 + x^2 = 6x^2\)[/tex]
- So, the simplified form is: [tex]\(-9x^3 + 6x^2 - 8x\)[/tex]
3. Simplify: [tex]\(x^5 - 24 - 5x^5 + 13\)[/tex]:
- Combine the like terms:
- [tex]\(x^5 - 5x^5 = -4x^5\)[/tex]
- [tex]\(-24 + 13 = -11\)[/tex]
- So, the simplified form is: [tex]\(-4x^5 - 11\)[/tex]
4. Simplify: [tex]\(-19x + 5 + 19x\)[/tex]:
- Combine the like terms:
- [tex]\(-19x + 19x = 0\)[/tex]
- The constant term remains [tex]\(+5\)[/tex]
- So, the simplified form is: [tex]\(5\)[/tex]
5. Simplify: [tex]\(26x^4 - 9 + 3x - 17x^2\)[/tex]:
- There are no like terms to combine.
- So, the simplified form is: [tex]\(26x^4 - 17x^2 + 3x - 9\)[/tex]
6. Simplify: [tex]\(7x - 19 - 6x - 24 + 13x^2\)[/tex]:
- Combine the like terms:
- [tex]\(7x - 6x = x\)[/tex]
- [tex]\(-19 - 24 = -43\)[/tex]
- So, the simplified form is: [tex]\(13x^2 + x - 43\)[/tex]
7. Simplify: [tex]\(-13x^3 - 9x + 27x^3\)[/tex]:
- Combine the like terms:
- [tex]\(-13x^3 + 27x^3 = 14x^3\)[/tex]
- So, the simplified form is: [tex]\(14x^3 - 9x\)[/tex]
8. Simplify: [tex]\(4x - 18 - 5x + 17\)[/tex]:
- Combine the like terms:
- [tex]\(4x - 5x = -x\)[/tex]
- [tex]\(-18 + 17 = -1\)[/tex]
- So, the simplified form is: [tex]\(-x - 1\)[/tex]
9. Simplify: [tex]\(39x^3 + 18x - 1 + 5x^4 - x^2 - x - 1\)[/tex]:
- Combine the like terms:
- [tex]\(18x - x = 17x\)[/tex]
- [tex]\(-1 - 1 = -2\)[/tex]
- So, the simplified form is: [tex]\(5x^4 + 39x^3 - x^2 + 17x - 2\)[/tex]
These are the simplified forms of the given polynomials. If you have any more questions or need further clarification, feel free to ask!
Thank you for reading the article Simplifying Polynomials Degree and Number of Terms1 Simplify tex 8x 2 x 2 20x 5 tex tex begin align 8x 20x 2 5 x 2. 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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