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Divide as indicated.\newline(x211x+36)÷(x5)(x^{2}-11x+36)\div(x-5)

Full solution

Q. Divide as indicated.\newline(x211x+36)÷(x5)(x^{2}-11x+36)\div(x-5)
  1. Set up division: Set up the long division.\newlineWe will divide the polynomial (x211x+36)(x^2 - 11x + 36) by the binomial (x5)(x - 5) using long division.
  2. Divide first term: Divide the first term of the dividend by the first term of the divisor. Divide x2x^2 by xx to get xx. This will be the first term of the quotient.
  3. Multiply divisor: Multiply the divisor by the first term of the quotient.\newlineMultiply (x5)(x - 5) by xx to get x25xx^2 - 5x. Write this below the dividend.
  4. Subtract result: Subtract the result from Step 33 from the dividend.\newlineSubtract (x25x)(x^2 - 5x) from (x211x+36)(x^2 - 11x + 36) to get 6x+36-6x + 36.
  5. Bring down next term: Bring down the next term of the dividend.\newlineThere are no more terms to bring down, so we continue with 6x+36-6x + 36.
  6. Divide new first term: Divide the new first term of the remaining dividend by the first term of the divisor.\newlineDivide 6x-6x by xx to get 6-6. This will be the next term of the quotient.
  7. Multiply new term: Multiply the divisor by the new term of the quotient.\newlineMultiply (x5)(x - 5) by 6-6 to get 6x+30-6x + 30. Write this below the remaining dividend.
  8. Subtract result: Subtract the result from Step 77 from the remaining dividend.\newlineSubtract (6x+30)(-6x + 30) from (6x+36)(-6x + 36) to get 66.
  9. Check remainder: Since the degree of the remainder (00) is less than the degree of the divisor (11), we cannot continue the division. The remainder is 66. The quotient is x6x - 6 with a remainder of 66.

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