Divide the polynomials. Your answer should be in the form p(x)+(k)/(x+4) where p is a polynomial and k is an integer. (x^(2)+1)/(x+4)=

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Divide the polynomials. Your answer should be in the form  p(x)+(k)/(x+4) where  p is a polynomial and  k is an integer.  (x^(2)+1)/(x+4)=

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Set up division: Set up the division of the polynomials in long division format. We will divide the polynomial x^2 + 1 by x + 4 using polynomial long division.Determine divisor count: Determine how many times the divisor (x + 4) goes into the first term of the dividend (x^2). The first term of the divisor x goes into the first term of the dividend x^2 exactly x times because x * x = x^2.Multiply and subtract: Multiply the entire divisor (x + 4) by the result from Step 2 (x) and subtract it from the dividend (x^2 + 1). Multiplying (x + 4) by x gives us x^2 + 4x. We subtract this from x^2 + 1 to find the remainder. (x^2 + 1) - (x^2 + 4x) = -4x + 1Bring down next term: Bring down the next term of the dividend, if any, and repeat the process. Since there are no more terms to bring down, we now have a remainder of -4x + 1.Write result in form: Write the result in the form p(x) + (k)/(x + 4) where p(x) is the quotient and k is the remainder. The quotient from our division is x and the remainder is -4x + 1. However, we need to express the remainder as a constant over the divisor (x + 4). To do this, we continue the division process to find the constant term.Determine remainder division: Determine how many times the divisor (x + 4) goes into the remainder (-4x + 1). The term -4x cannot be divided by x + 4 to give a polynomial term, so we stop the division here. The remainder is -4x + 1.Express remainder as fraction: Express the remainder as a fraction over the divisor (x + 4). The remainder is -4x + 1, so we write it as (-4x + 1)/(x + 4).Final answer: Since we cannot simplify the remainder further, we have our final answer. The final answer is p(x) + (k)/(x + 4) where p(x) = x and k = -4x + 1.

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

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