Answer :
Sure, let's go through each of the polynomials step-by-step to understand how we arrive at the solutions:
35. Divide [tex]\((9x - 6) / 3\)[/tex]:
- Factor 3 out of the numerator: [tex]\(9x - 6 = 3(3x - 2)\)[/tex].
- Simplify: [tex]\((3(3x - 2)) / 3 = 3x - 2\)[/tex].
36. Divide [tex]\((4x - 7) / 2\)[/tex]:
- Simplify each term separately: [tex]\((4x / 2) - (7 / 2)\)[/tex].
- The result is: [tex]\(2x - \frac{7}{2}\)[/tex].
37. Divide [tex]\((x^2 - 3x + 5) / x\)[/tex]:
- Divide each term by [tex]\(x\)[/tex]: [tex]\((x^2 / x) - (3x / x) + (5 / x)\)[/tex].
- The result is: [tex]\(x - 3 + \frac{5}{x}\)[/tex].
38. Divide [tex]\((5x^2 - 25x + 2) / -5x\)[/tex]:
- Divide each term by [tex]\(-5x\)[/tex]: [tex]\((5x^2 / -5x) - (25x / -5x) + (2 / -5x)\)[/tex].
- Simplify: [tex]\(-x + 5 - \frac{2}{5x}\)[/tex].
39. Divide [tex]\((4x^{10} - 5x^9 - 20x^4) / 4x^2\)[/tex]:
- Divide each term by [tex]\(4x^2\)[/tex]: [tex]\((4x^{10} / 4x^2) - (5x^9 / 4x^2) - (20x^4 / 4x^2)\)[/tex].
- Simplify: [tex]\(x^{8} - \frac{5}{4}x^{7} - 5x^2\)[/tex].
40. Divide [tex]\((-x^6 + x^5 + 7x^2 - 9) / x^4\)[/tex]:
- Divide each term by [tex]\(x^4\)[/tex]: [tex]\((-x^6 / x^4) + (x^5 / x^4) + (7x^2 / x^4) - (9 / x^4)\)[/tex].
- Simplify: [tex]\(-x^2 + x + \frac{7}{x^2} - \frac{9}{x^4}\)[/tex].
41. Divide [tex]\((x^2 + 2x + 6) / x\)[/tex]:
- Divide each term by [tex]\(x\)[/tex]: [tex]\((x^2 / x) + (2x / x) + (6 / x)\)[/tex].
- Simplify: [tex]\(x + 2 + \frac{6}{x}\)[/tex].
42. Divide [tex]\((3x^2 - 15x + 5) / -3x\)[/tex]:
- Divide each term by [tex]\(-3x\)[/tex]: [tex]\((3x^2 / -3x) - (15x / -3x) + (5 / -3x)\)[/tex].
- Simplify: [tex]\(-x + 5 - \frac{5}{3x}\)[/tex].
43. Divide [tex]\((2x^{11} - 5x^7 - 10x^6) / 2x^3\)[/tex]:
- Divide each term by [tex]\(2x^3\)[/tex]: [tex]\((2x^{11} / 2x^3) - (5x^7 / 2x^3) - (10x^6 / 2x^3)\)[/tex].
- Simplify: [tex]\(x^8 - \frac{5}{2}x^4 - 5x^3\)[/tex].
44. Divide [tex]\((-2x^6 + 5x^5 + 9x^2 + 2) / x^4\)[/tex]:
- Divide each term by [tex]\(x^4\)[/tex]: [tex]\((-2x^6 / x^4) + (5x^5 / x^4) + (9x^2 / x^4) + (2 / x^4)\)[/tex].
- Simplify: [tex]\(-2x^2 + 5x + \frac{9}{x^2} + \frac{2}{x^4}\)[/tex].
Each division has been performed by considering each term of the polynomial individually, dividing by the denominator, and simplifying the result accordingly.
35. Divide [tex]\((9x - 6) / 3\)[/tex]:
- Factor 3 out of the numerator: [tex]\(9x - 6 = 3(3x - 2)\)[/tex].
- Simplify: [tex]\((3(3x - 2)) / 3 = 3x - 2\)[/tex].
36. Divide [tex]\((4x - 7) / 2\)[/tex]:
- Simplify each term separately: [tex]\((4x / 2) - (7 / 2)\)[/tex].
- The result is: [tex]\(2x - \frac{7}{2}\)[/tex].
37. Divide [tex]\((x^2 - 3x + 5) / x\)[/tex]:
- Divide each term by [tex]\(x\)[/tex]: [tex]\((x^2 / x) - (3x / x) + (5 / x)\)[/tex].
- The result is: [tex]\(x - 3 + \frac{5}{x}\)[/tex].
38. Divide [tex]\((5x^2 - 25x + 2) / -5x\)[/tex]:
- Divide each term by [tex]\(-5x\)[/tex]: [tex]\((5x^2 / -5x) - (25x / -5x) + (2 / -5x)\)[/tex].
- Simplify: [tex]\(-x + 5 - \frac{2}{5x}\)[/tex].
39. Divide [tex]\((4x^{10} - 5x^9 - 20x^4) / 4x^2\)[/tex]:
- Divide each term by [tex]\(4x^2\)[/tex]: [tex]\((4x^{10} / 4x^2) - (5x^9 / 4x^2) - (20x^4 / 4x^2)\)[/tex].
- Simplify: [tex]\(x^{8} - \frac{5}{4}x^{7} - 5x^2\)[/tex].
40. Divide [tex]\((-x^6 + x^5 + 7x^2 - 9) / x^4\)[/tex]:
- Divide each term by [tex]\(x^4\)[/tex]: [tex]\((-x^6 / x^4) + (x^5 / x^4) + (7x^2 / x^4) - (9 / x^4)\)[/tex].
- Simplify: [tex]\(-x^2 + x + \frac{7}{x^2} - \frac{9}{x^4}\)[/tex].
41. Divide [tex]\((x^2 + 2x + 6) / x\)[/tex]:
- Divide each term by [tex]\(x\)[/tex]: [tex]\((x^2 / x) + (2x / x) + (6 / x)\)[/tex].
- Simplify: [tex]\(x + 2 + \frac{6}{x}\)[/tex].
42. Divide [tex]\((3x^2 - 15x + 5) / -3x\)[/tex]:
- Divide each term by [tex]\(-3x\)[/tex]: [tex]\((3x^2 / -3x) - (15x / -3x) + (5 / -3x)\)[/tex].
- Simplify: [tex]\(-x + 5 - \frac{5}{3x}\)[/tex].
43. Divide [tex]\((2x^{11} - 5x^7 - 10x^6) / 2x^3\)[/tex]:
- Divide each term by [tex]\(2x^3\)[/tex]: [tex]\((2x^{11} / 2x^3) - (5x^7 / 2x^3) - (10x^6 / 2x^3)\)[/tex].
- Simplify: [tex]\(x^8 - \frac{5}{2}x^4 - 5x^3\)[/tex].
44. Divide [tex]\((-2x^6 + 5x^5 + 9x^2 + 2) / x^4\)[/tex]:
- Divide each term by [tex]\(x^4\)[/tex]: [tex]\((-2x^6 / x^4) + (5x^5 / x^4) + (9x^2 / x^4) + (2 / x^4)\)[/tex].
- Simplify: [tex]\(-2x^2 + 5x + \frac{9}{x^2} + \frac{2}{x^4}\)[/tex].
Each division has been performed by considering each term of the polynomial individually, dividing by the denominator, and simplifying the result accordingly.
