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Division of a Polynomial by a Monomial

Solve the fol...

Question

Solve the following when $x^{3} + 3 x^{2} + 3 x + 1$ is divisible by
$x$

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Solution

$(x^{3} + 3 x^{2} + 3 x + 1) \div x = \frac{x^{3} + 3 x^{2} + 3 x + 1}{x}$
$= \frac{x (x^{2} + 3 x + 3)}{x} + \frac{1}{x}$
$= x^{2} + 3 x + 3 + \frac{1}{x}$

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