1. **Problem statement:** Simplify and arrange the polynomial $P(x) = 3x^3 + 5x - 12 - x^2 + x^3 - 6x^2 - 2x$ in ascending powers of $x$. 2. **Combine like terms:** $$P(x) = (3x^3 + x^3) + (-x^2 - 6x^2) + (5x - 2x) - 12$$ $$= 4x^3 - 7x^2 + 3x - 12$$ 3. **Arrange in ascending powers:** $$P(x) = -12 + 3x - 7x^2 + 4x^3$$ This is the simplified and arranged form of $P(x)$.