The problem asks us to divide the polynomial $24x^4 - 8x^3 + 48x^2$ by the monomial $-8x$.

1. Problem Description

The problem asks us to divide the polynomial $24x^4 - 8x^3 + 48x^2$ by the monomial $-8x$.

2. Solution Steps

We need to divide each term of the polynomial by $-8x$.

$\frac{24x^4 - 8x^3 + 48x^2}{-8x} = \frac{24x^4}{-8x} - \frac{8x^3}{8x} + \frac{48x^2}{-8x}$

First, divide $24x^4$ by $-8x$:

$\frac{24x^4}{-8x} = -3x^{4-1} = -3x^3$

Second, divide $-8x^3$ by $-8x$:

$\frac{-8x^3}{-8x} = x^{3-1} = x^2$

Third, divide $48x^2$ by $-8x$:

$\frac{48x^2}{-8x} = -6x^{2-1} = -6x$

Combining the results, we get:

$-3x^3 + x^2 - 6x$

3. Final Answer

$-3x^3+x^2-6x$