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{6x^2 - 4x - 3}{x} = $

Explanation:

Step1: Split the fraction

We can split the numerator into three separate fractions over the denominator \( x \):
\[
\frac{6x^2 - 4x - 3}{x}=\frac{6x^2}{x}-\frac{4x}{x}-\frac{3}{x}
\]

Step2: Simplify each fraction

Simplify each term:

• For \( \frac{6x^2}{x} \), using the rule \( \frac{x^m}{x^n}=x^{m - n} \) (here \( m = 2 \), \( n = 1 \)), we get \( 6x^{2-1}=6x \).
• For \( \frac{4x}{x} \), we get \( 4 \) (since \( x/x = 1 \)).
• The last term remains \( -\frac{3}{x} \).

Combining these simplified terms, we have \( 6x - 4-\frac{3}{x} \), which is in the form \( p(x)+\frac{k}{x} \) where \( p(x)=6x - 4 \) and \( k=- 3 \).

Answer:

\( 6x - 4+\frac{-3}{x} \) (or equivalently \( 6x - 4-\frac{3}{x} \))