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!
