Divide the following polynomials: $$ \begin{array}{ll} ext { 35. } \frac{9 x-6}{3} & ext { 45. } \frac{f^{3}+64}{f+4} \ ext { 36. } \frac{4 x-7}{2} & ext { 46. } \frac{4 p-2+3 p^{2}}{p-1} \ ext { 37. } \frac{x^{2}-3 x+5}{x} & ext { 47. } \frac{3 m-4+2 m^{2}}{m+5} \ ext { 38. } \frac{5 x^{2}-25 x+2}{-5 x} & ext { 48. } \frac{f^{3}-64}{f-4} \ ext { 39. } \frac{4 x^{10}-5 x^{9}-20 x^{4}}{4 x^{2}} & ext { 49. } \frac{-5 p+4 p^{2}+4}{p-2} \ ext { 40. }\left(-x^{6}+x^{5}+7 x^{2}-9 ight) \div x^{4} \ ext { 41. }\left(x^{2}+2 x+6 ight) \div x & ext { 50. }\left(4 p+3 p^{2}-1 ight) \div(p+4) \ ext { 42. }\left(3 x^{2}-15 x+5 ight) \div(-3 x) & ext { 51. }\left(20 x^{2}-13 x+2 ight) \div(5 x-2) \ ext { 43. }\left(2 x^{11}-5 x^{7}-10 x^{6} ight) \div 2 x^{3} & ext { 52. }\left(12 x^{2}-6 x^{3}-3-9 x ight) \div(3 x-3) \ ext { 44. }\left(-2 x^{6}+5 x^{5}+9 x^{2}+2 ight) \div x^{4} & ext { 53. }\left(8 x^{2}-2 x-3 ight) \div(2 x+1) \ & ext { 54. }\left(-3 x^{2}+6 x^{3}-4-x ight) \div(2 x+1)\end{array} $$

Question

Divide the following polynomials: $$ \begin{array}{ll}	ext { 35. } \frac{9 x-6}{3} & 	ext { 45. } \frac{f^{3}+64}{f+4} \ 	ext { 36. } \frac{4 x-7}{2} & 	ext { 46. } \frac{4 p-2+3 p^{2}}{p-1} \ 	ext { 37. } \frac{x^{2}-3 x+5}{x} & 	ext { 47. } \frac{3 m-4+2 m^{2}}{m+5} \ 	ext { 38. } \frac{5 x^{2}-25 x+2}{-5 x} & 	ext { 48. } \frac{f^{3}-64}{f-4} \ 	ext { 39. } \frac{4 x^{10}-5 x^{9}-20 x^{4}}{4 x^{2}} & 	ext { 49. } \frac{-5 p+4 p^{2}+4}{p-2} \ 	ext { 40. }\left(-x^{6}+x^{5}+7 x^{2}-9ight) \div x^{4} \ 	ext { 41. }\left(x^{2}+2 x+6ight) \div x & 	ext { 50. }\left(4 p+3 p^{2}-1ight) \div(p+4) \ 	ext { 42. }\left(3 x^{2}-15 x+5ight) \div(-3 x) & 	ext { 51. }\left(20 x^{2}-13 x+2ight) \div(5 x-2) \ 	ext { 43. }\left(2 x^{11}-5 x^{7}-10 x^{6}ight) \div 2 x^{3} & 	ext { 52. }\left(12 x^{2}-6 x^{3}-3-9 xight) \div(3 x-3) \ 	ext { 44. }\left(-2 x^{6}+5 x^{5}+9 x^{2}+2ight) \div x^{4} & 	ext { 53. }\left(8 x^{2}-2 x-3ight) \div(2 x+1) \ & 	ext { 54. }\left(-3 x^{2}+6 x^{3}-4-xight) \div(2 x+1)\end{array} $$

UpStudy AI · Accepted Answer

Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{-x^{6}+x^{5}+7x^{2}-9}{x^{4}}$$
- step1: Calculate:
  $$-x^{2}+x+\frac{7x^{2}-9}{x^{4}}$$
Calculate or simplify the expression $$ \frac{-3 x^{2}+6 x^{3}-4-x}{2 x+1} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{-3x^{2}+6x^{3}-4-x}{2x+1}$$
- step1: Calculate:
  $$3x^{2}-3x+1+\frac{-5}{2x+1}$$
Calculate or simplify the expression $$ \frac{4 p+3 p^{2}-1}{p+4} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{4p+3p^{2}-1}{p+4}$$
- step1: Calculate:
  $$3p-8+\frac{31}{p+4}$$
Calculate or simplify the expression $$ \frac{3 m-4+2 m^{2}}{m+5} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{3m-4+2m^{2}}{m+5}$$
- step1: Calculate:
  $$2m-7+\frac{31}{m+5}$$
Calculate or simplify the expression $$ \frac{-5 p+4 p^{2}+4}{p-2} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{-5p+4p^{2}+4}{p-2}$$
- step1: Calculate:
  $$4p+3+\frac{10}{p-2}$$
Calculate or simplify the expression $$ \frac{x^{2}-3 x+5}{x} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{x^{2}-3x+5}{x}$$
- step1: Calculate:
  $$x-3+\frac{5}{x}$$
Calculate or simplify the expression $$ \frac{f^{3}-64}{f-4} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{f^{3}-64}{f-4}$$
- step1: Calculate:
  $$\frac{\left(f-4\right)\left(f^{2}+4f+16\right)}{f-4}$$
- step2: Reduce the fraction:
  $$f^{2}+4f+16$$
Calculate or simplify the expression $$ \frac{9 x-6}{3} $$.
Divide by following steps:
- step0: Divide the numbers:
  $$\frac{9x-6}{3}$$
- step1: Calculate:
  $$3x-2$$
Calculate or simplify the expression $$ \frac{4 x-7}{2} $$.
Divide by following steps:
- step0: Divide the numbers:
  $$\frac{4x-7}{2}$$
- step1: Calculate:
  $$2x-\frac{7}{2}$$
Calculate or simplify the expression $$ \frac{20 x^{2}-13 x+2}{5 x-2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{20x^{2}-13x+2}{5x-2}$$
- step1: Factor the expression:
  $$\frac{\left(5x-2\right)\left(4x-1\right)}{5x-2}$$
- step2: Reduce the fraction:
  $$4x-1$$
Calculate or simplify the expression $$ \frac{2 x^{11}-5 x^{7}-10 x^{6}}{2 x^{3}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{2x^{11}-5x^{7}-10x^{6}}{2x^{3}}$$
- step1: Factor:
  $$\frac{x^{3}\left(2x^{8}-5x^{4}-10x^{3}\right)}{2x^{3}}$$
- step2: Reduce the fraction:
  $$\frac{2x^{8}-5x^{4}-10x^{3}}{2}$$
Calculate or simplify the expression $$ \frac{12 x^{2}-6 x^{3}-3-9 x}{3 x-3} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{12x^{2}-6x^{3}-3-9x}{3x-3}$$
- step1: Factor the expression:
  $$\frac{3\left(4x^{2}-2x^{3}-1-3x\right)}{3\left(x-1\right)}$$
- step2: Reduce the fraction:
  $$\frac{4x^{2}-2x^{3}-1-3x}{x-1}$$
Calculate or simplify the expression $$ \frac{x^{2}+2 x+6}{x} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{x^{2}+2x+6}{x}$$
- step1: Calculate:
  $$x+2+\frac{6}{x}$$
Calculate or simplify the expression $$ \frac{3 x^{2}-15 x+5}{-3 x} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{3x^{2}-15x+5}{-3x}$$
- step1: Calculate:
  $$-x+5+\frac{5}{-3x}$$
Calculate or simplify the expression $$ \frac{5 x^{2}-25 x+2}{-5 x} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{5x^{2}-25x+2}{-5x}$$
- step1: Calculate:
  $$-x+5+\frac{2}{-5x}$$
Calculate or simplify the expression $$ \frac{8 x^{2}-2 x-3}{2 x+1} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{8x^{2}-2x-3}{2x+1}$$
- step1: Factor the expression:
  $$\frac{\left(2x+1\right)\left(4x-3\right)}{2x+1}$$
- step2: Reduce the fraction:
  $$4x-3$$
Calculate or simplify the expression $$ \frac{-2 x^{6}+5 x^{5}+9 x^{2}+2}{x^{4}} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{-2x^{6}+5x^{5}+9x^{2}+2}{x^{4}}$$
- step1: Calculate:
  $$-2x^{2}+5x+\frac{9x^{2}+2}{x^{4}}$$
Calculate or simplify the expression $$ \frac{f^{3}+64}{f+4} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{f^{3}+64}{f+4}$$
- step1: Calculate:
  $$\frac{\left(f+4\right)\left(f^{2}-4f+16\right)}{f+4}$$
- step2: Reduce the fraction:
  $$f^{2}-4f+16$$
Calculate or simplify the expression $$ \frac{4 p-2+3 p^{2}}{p-1} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{4p-2+3p^{2}}{p-1}$$
- step1: Calculate:
  $$3p+7+\frac{5}{p-1}$$
Calculate or simplify the expression $$ \frac{4 x^{10}-5 x^{9}-20 x^{4}}{4 x^{2}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{4x^{10}-5x^{9}-20x^{4}}{4x^{2}}$$
- step1: Factor:
  $$\frac{x^{2}\left(4x^{8}-5x^{7}-20x^{2}\right)}{4x^{2}}$$
- step2: Reduce the fraction:
  $$\frac{4x^{8}-5x^{7}-20x^{2}}{4}$$
Here are the results of the polynomial divisions:

1. $$ \frac{9x - 6}{3} = 3x - 2 $$
2. $$ \frac{4x - 7}{2} = 2x - \frac{7}{2} $$
3. $$ \frac{x^{2} - 3x + 5}{x} = x - 3 + \frac{5}{x} $$
4. $$ \frac{5x^{2} - 25x + 2}{-5x} = -x + 5 + \frac{2}{-5x} $$
5. $$ \frac{4x^{10} - 5x^{9} - 20x^{4}}{4x^{2}} = \frac{4x^{8} - 5x^{7} - 20x^{2}}{4} $$
6. $$ \left(-x^{6} + x^{5} + 7x^{2} - 9\right) \div x^{4} = -x^{2} + x + \frac{7x^{2} - 9}{x^{4}} $$
7. $$ \frac{x^{2} + 2x + 6}{x} = x + 2 + \frac{6}{x} $$
8. $$ \frac{3m - 4 + 2m^{2}}{m + 5} = 2m - 7 + \frac{31}{m + 5} $$
9. $$ \frac{f^{3} + 64}{f + 4} = f^{2} - 4f + 16 $$
10. $$ \frac{f^{3} - 64}{f - 4} = f^{2} + 4f + 16 $$
11. $$ \frac{-5p + 4p^{2} + 4}{p - 2} = 4p + 3 + \frac{10}{p - 2} $$
12. $$ \frac{4p - 2 + 3p^{2}}{p - 1} = 3p + 7 + \frac{5}{p - 1} $$
13. $$ \frac{20x^{2} - 13x + 2}{5x - 2} = 4x - 1 $$
14. $$ \frac{12x^{2} - 6x^{3} - 3 - 9x}{3x - 3} = \frac{4x^{2} - 2x^{3} - 1 - 3x}{x - 1} $$
15. $$ \frac{8x^{2} - 2x - 3}{2x + 1} = 4x - 3 $$
16. $$ \frac{-3x^{2} + 6x^{3} - 4 - x}{2x + 1} = 3x^{2} - 3x + 1 + \frac{-5}{2x + 1} $$

If you need further assistance or explanations for any specific division, feel free to ask!
Here are the simplified results of the polynomial divisions: 1. $$ \frac{9x - 6}{3} = 3x - 2 $$ 2. $$ \frac{4x - 7}{2} = 2x - 3.5 $$ 3. $$ \frac{x^{2} - 3x + 5}{x} = x - 3 + \frac{5}{x} $$ 4. $$ \frac{5x^{2} - 25x + 2}{-5x} = -x + 5 - \frac{2}{5x} $$ 5. $$ \frac{4x^{10} - 5x^{9} - 20x^{4}}{4x^{2}} = x^{8} - \frac{5}{4}x^{7} - 5x^{2} $$ 6. $$ \left(-x^{6} + x^{5} + 7x^{2} - 9\right) \div x^{4} = -x^{2} + x + \frac{7x^{2} - 9}{x^{4}} $$ 7. $$ \frac{x^{2} + 2x + 6}{x} = x + 2 + \frac{6}{x} $$ 8. $$ \frac{3m - 4 + 2m^{2}}{m + 5} = 2m - 7 + \frac{31}{m + 5} $$ 9. $$ \frac{f^{3} + 64}{f + 4} = f^{2} - 4f + 16 $$ 10. $$ \frac{f^{3} - 64}{f - 4} = f^{2} + 4f + 16 $$ 11. $$ \frac{-5p + 4p^{2} + 4}{p - 2} = 4p + 3 + \frac{10}{p - 2} $$ 12. $$ \frac{4p - 2 + 3p^{2}}{p - 1} = 3p + 7 + \frac{5}{p - 1} $$ 13. $$ \frac{20x^{2} - 13x + 2}{5x - 2} = 4x - 1 $$ 14. $$ \frac{12x^{2} - 6x^{3} - 3 - 9x}{3x - 3} = \frac{4x^{2} - 2x^{3} - 1 - 3x}{x - 1} $$ 15. $$ \frac{8x^{2} - 2x - 3}{2x + 1} = 4x - 3 $$ 16. $$ \frac{-3x^{2} + 6x^{3} - 4 - x}{2x + 1} = 3x^{2} - 3x + 1 + \frac{-5}{2x + 1} $$ If you need further assistance or explanations for any specific division, feel free to ask!

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