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{3x^2 - 10}{x} = $

Explanation:

Step1: Split the fraction

We can split the fraction \(\frac{3x^2 - 10}{x}\) into two separate fractions: \(\frac{3x^2}{x}-\frac{10}{x}\).

Step2: Simplify each fraction

For the first fraction \(\frac{3x^2}{x}\), using the rule of exponents \(\frac{x^m}{x^n}=x^{m - n}\) (where \(m = 2\) and \(n=1\)), we get \(3x^{2-1}=3x\). For the second fraction \(\frac{10}{x}\), we can rewrite it as \(\frac{- 10}{x}\) (since \(-\frac{10}{x}=\frac{-10}{x}\)). So combining these, we have \(3x+\frac{- 10}{x}\).

Answer:

\(3x+\frac{-10}{x}\)