Thank you for visiting Divide the following polynomials 35 tex frac 9x 6 3 tex 36 tex frac 4x 7 2 tex 37 tex frac x 2 3x 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 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.
Thank you for reading the article Divide the following polynomials 35 tex frac 9x 6 3 tex 36 tex frac 4x 7 2 tex 37 tex frac x 2 3x 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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