Question: Divide the following expression.
$$\frac{6x^3+8x^2-10x}{2x}$$
Answer choices:
- $$3x^2+4x-5$$
- $$x^2+4x-10$$
- $$3x^2+4x-10$$
- $$x^2+4x-5$$
1. **State the problem:** We need to divide the polynomial expression $$6x^3+8x^2-10x$$ by $$2x$$.
2. **Write the division as a fraction:**
$$\frac{6x^3+8x^2-10x}{2x}$$
3. **Divide each term in the numerator by the denominator:**
$$\frac{6x^3}{2x} + \frac{8x^2}{2x} - \frac{10x}{2x}$$
4. **Simplify each term:**
- $$\frac{6x^3}{2x} = 3x^{3-1} = 3x^2$$
- $$\frac{8x^2}{2x} = 4x^{2-1} = 4x$$
- $$\frac{10x}{2x} = 5$$
5. **Combine the simplified terms:**
$$3x^2 + 4x - 5$$
6. **Final answer:** The expression simplifies to $$3x^2 + 4x - 5$$.
This matches the first answer choice.