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Divide the polynomials. Your answer should be in the form 
p(x)+(k)/(x-1) where 
p is a polynomial and 
k is an integer.

(x^(2)+6x-4)/(x-1)=

Divide the polynomials. Your answer should be in the form p(x)+kx1 p(x)+\frac{k}{x-1} where p p is a polynomial and k k is an integer.\newlinex2+6x4x1= \frac{x^{2}+6 x-4}{x-1}=

Full solution

Q. Divide the polynomials. Your answer should be in the form p(x)+kx1 p(x)+\frac{k}{x-1} where p p is a polynomial and k k is an integer.\newlinex2+6x4x1= \frac{x^{2}+6 x-4}{x-1}=
  1. Set up long division: Set up the long division.\newlineWe will use long division to divide the polynomial x2+6x4x^2 + 6x - 4 by x1x - 1.
  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 and quotient: Multiply the divisor by the first term of the quotient.\newlineMultiply x1x - 1 by xx to get x2xx^2 - x.
  4. Subtract result: Subtract the result from the dividend.\newlineSubtract x2xx^2 - x from x2+6x4x^2 + 6x - 4 to get 7x47x - 4.
  5. Bring down next term: Bring down the next term. Since there are no more terms to bring down, we proceed to the next step.
  6. Divide new term: Divide the new term by the first term of the divisor.\newlineDivide 7x7x by xx to get 77. This will be the next term of the quotient.
  7. Multiply divisor and new term: Multiply the divisor by the new term of the quotient.\newlineMultiply x1x - 1 by 77 to get 7x77x - 7.
  8. Subtract result: Subtract the result from the new term of the dividend.\newlineSubtract 7x77x - 7 from 7x47x - 4 to get 33.
  9. Check degree of remainder: Since the degree of the remainder (00) is less than the degree of the divisor (11), we cannot continue the division.\newlineThe remainder is 33, and the quotient is x+7x + 7.
  10. Write final answer: Write the final answer in the form p(x)+kx1p(x) + \frac{k}{x - 1}.\newlineThe quotient is x+7x + 7 and the remainder is 33, so the final answer is p(x)=x+7p(x) = x + 7 and k=3k = 3.