Question

divide the polynomials.
your answer should be in the form $p(x) + \frac{k}{x}$ where $p$ is a polynomial and $k$ is an integer.
$\frac{x^5 + 6x + 2}{x} = $

Explanation:

Step1: Divide each term by \( x \)

We have the polynomial \( \frac{x^5 + 6x + 2}{x} \). Using the rule of dividing each term in the numerator by the denominator, we get \( \frac{x^5}{x}+\frac{6x}{x}+\frac{2}{x} \).

Step2: Simplify each term

Simplify each fraction: \( \frac{x^5}{x}=x^{5 - 1}=x^4 \), \( \frac{6x}{x}=6 \), and \( \frac{2}{x} \) remains as it is. So combining these, we have \( x^4 + 6+\frac{2}{x} \).

Answer:

\( x^4 + 6 + \frac{2}{x} \)