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Divide the polynomials.
The form of your answer should either be 
p(x) or 
p(x)+(k)/(x-5) where 
p(x) is a polynomial and 
k is an integer.

(2x^(3)-11x^(2)+25)/(x-5)=

Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) or p(x)+kx5 p(x)+\frac{k}{x-5} where p(x) p(x) is a polynomial and k k is an integer.\newline2x311x2+25x5= \frac{2 x^{3}-11 x^{2}+25}{x-5}=

Full solution

Q. Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) or p(x)+kx5 p(x)+\frac{k}{x-5} where p(x) p(x) is a polynomial and k k is an integer.\newline2x311x2+25x5= \frac{2 x^{3}-11 x^{2}+25}{x-5}=
  1. Set up long division: Set up the long division.\newlineWe will use polynomial long division to divide (2x311x2+25)(2x^3 - 11x^2 + 25) by (x5)(x - 5).
  2. Divide first term: Divide the first term of the numerator by the first term of the denominator.\newlineDivide 2x32x^3 by xx to get 2x22x^2.\newlineWrite 2x22x^2 above the division bar.
  3. Multiply divisor and result: Multiply the divisor (x5)(x - 5) by the result from Step 22 (2x2)(2x^2).\newline2x2(x5)=2x310x2.2x^2 \cdot (x - 5) = 2x^3 - 10x^2.\newlineWrite this result under the corresponding terms of the dividend.
  4. Subtract result from dividend: Subtract the result from Step 33 from the corresponding terms of the dividend.\newline(2x311x2)(2x310x2)=x2(2x^3 - 11x^2) - (2x^3 - 10x^2) = -x^2.\newlineBring down the next term of the dividend, which is +25+25.
  5. Bring down next term: Divide the result from Step 44 by the first term of the divisor.\newlineDivide x2-x^2 by xx to get x-x.\newlineWrite x-x above the division bar next to 2x22x^2.
  6. Divide result by first term: Multiply the divisor (x5)(x - 5) by the result from Step 55 (x)(-x).\newlinex×(x5)=x2+5x-x \times (x - 5) = -x^2 + 5x.\newlineWrite this result under the corresponding terms of the dividend.
  7. Multiply divisor and result: Subtract the result from Step 66 from the corresponding terms of the dividend.\newline(x2+25)(x2+5x)=5x+25(-x^2 + 25) - (-x^2 + 5x) = -5x + 25.
  8. Subtract result from dividend: Divide the result from Step 77 by the first term of the divisor.\newlineDivide 5x-5x by xx to get 5-5.\newlineWrite 5-5 above the division bar next to 2x2x2x^2 - x.
  9. Divide result by first term: Multiply the divisor (x5)(x - 5) by the result from Step 88 (5)(-5).\newline5×(x5)=5x+25-5 \times (x - 5) = -5x + 25.\newlineWrite this result under the corresponding terms of the dividend.
  10. Multiply divisor and result: Subtract the result from Step 99 from the corresponding terms of the dividend.\newline(5x+25)(5x+25)=0(-5x + 25) - (-5x + 25) = 0.\newlineThere is no remainder, so the division is complete.