Divide the polynomials. Your answer should be in the form p(x)+(k)/(x-2) where p is a polynomial and k is an integer. (x^(2)-5)/(x-2)=

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Divide the polynomials. Your answer should be in the form  p(x)+(k)/(x-2) where  p is a polynomial and  k is an integer.  (x^(2)-5)/(x-2)=

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Set up division: Set up the division of the polynomials in long division format. We will divide (x^2 - 5) by (x - 2) using polynomial long division.Divide first term: Divide the first term of the dividend by the first term of the divisor. Divide x^2 by x to get x. This will be the first term of the quotient polynomial p(x). Calculation: x^2 / x = xMultiply and subtract: Multiply the divisor by the result from Step 2 and subtract from the dividend. Multiply (x - 2) by x to get (x^2 - 2x). Subtract this from (x^2 - 5). Calculation: (x^2 - 5) - (x^2 - 2x) = 2x - 5Bring down next term: Bring down the next term of the dividend, if any. Since there are no more terms to bring down, we proceed to the next step.Divide result: Divide the result from Step 3 by the first term of the divisor. Divide 2x by x to get 2. This will be the next term of the quotient polynomial p(x). Calculation: 2x / x = 2Multiply and subtract: Multiply the divisor by the result from Step 5 and subtract from the result of Step 3. Multiply (x - 2) by 2 to get (2x - 4). Subtract this from (2x - 5). Calculation: (2x - 5) - (2x - 4) = -1Check for completion: Since the degree of the remainder (-1) is less than the degree of the divisor (x - 2), we cannot continue the division. The remainder is -1, and this will be the value of k in the final answer.Write final answer: Write the final answer in the form p(x) + (k)/(x - 2). The quotient polynomial p(x) is x + 2, and the remainder is -1. Final Answer: p(x) = x + 2, k = -1

Divide the polynomials. Your answer should be in the form $p(x)+\frac{k}{x-2}$ where $p$ is a polynomial and $k$ is an integer. $\newline$ $\frac{x^{2}-5}{x-2}=$

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Divide the polynomials. Your answer should be in the form $p(x)+\frac{k}{x-2}$ where $p$ is a polynomial and $k$ is an integer. $\newline$ $\frac{x^{2}-5}{x-2}=$