Question: User: $(x-4)\times(2x^2+3x-2)$
1. **State the problem:** Simplify the expression $$(x-4)\times(2x^2+3x-2)$$.
2. **Formula and rules:** Use the distributive property (also called FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.
3. **Distribute:**
$$x \times (2x^2+3x-2) = 2x^3 + 3x^2 - 2x$$
$$-4 \times (2x^2+3x-2) = -8x^2 - 12x + 8$$
4. **Combine like terms:**
$$2x^3 + 3x^2 - 2x - 8x^2 - 12x + 8$$
5. **Simplify:**
$$2x^3 + (3x^2 - 8x^2) + (-2x - 12x) + 8 = 2x^3 - 5x^2 - 14x + 8$$
**Final answer:**
$$2x^3 - 5x^2 - 14x + 8$$