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)+2)/(x-1)=

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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)+2)/(x-1)=

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Set up division: Set up the division of the polynomials in long division format. We are dividing x^2 + 2 by x - 1. We write this as (x^2 + 0x + 2) ÷ (x - 1) to make sure we account for all terms.Divide first term: Divide the first term of the dividend by the first term of the divisor. We divide x^2 by x to get x. This will be the first term of the quotient polynomial p(x).Multiply and subtract: Multiply the divisor by the term obtained in Step 2 and subtract from the dividend. We multiply (x - 1) by x to get (x^2 - x). We then subtract this from x^2 + 0x + 2. (x^2 + 0x + 2) - (x^2 - x) = x^2 + 0x + 2 - x^2 + x = x + 2.Bring down next term: Bring down the next term of the dividend, if any, and repeat the division process. Since there are no more terms to bring down, we proceed with x + 2 as our new dividend.Divide obtained term: Divide the term obtained after subtraction by the first term of the divisor. We divide x by x to get 1. This will be the next term of the quotient polynomial p(x).Multiply and subtract: Multiply the divisor by the term obtained in Step 5 and subtract from the new dividend. We multiply (x - 1) by 1 to get (x - 1). We then subtract this from x + 2. (x + 2) - (x - 1) = x + 2 - x + 1 = 3.Find remainder: Since we cannot divide 3 by x - 1 anymore, 3 is the remainder of the division. The remainder 3 cannot be divided further by x - 1, so we express it as a fraction over the divisor.Write final answer: Write the final answer in the form p(x) + (k)/(x - 1). The quotient polynomial p(x) is x + 1 and the remainder is 3, so the final answer is x + 1 + 3/(x - 1).

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

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