Polynomial Multiplication 22A4C7

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. **Multiply each term:** $$x \times 2x^2 = 2x^3$$ $$x \times 3x = 3x^2$$ $$x \times (-2) = -2x$$ $$-4 \times 2x^2 = -8x^2$$ $$-4 \times 3x = -12x$$ $$-4 \times (-2) = 8$$ 4. **Combine all terms:** $$2x^3 + 3x^2 - 2x - 8x^2 - 12x + 8$$ 5. **Group like terms:** $$2x^3 + (3x^2 - 8x^2) + (-2x - 12x) + 8$$ 6. **Simplify:** $$2x^3 - 5x^2 - 14x + 8$$ **Final answer:** $$2x^3 - 5x^2 - 14x + 8$$