1. **State the problem:** Find the function $(g - h)(x)$ where $g(x) = 2x - 3$ and $h(x) = x^3 - 2x^2 + 2x$. 2. **Recall the formula:** The difference of two functions is given by $$ (g - h)(x) = g(x) - h(x) $$ 3. **Substitute the given functions:** $$ (g - h)(x) = (2x - 3) - (x^3 - 2x^2 + 2x) $$ 4. **Distribute the minus sign:** $$ (g - h)(x) = 2x - 3 - x^3 + 2x^2 - 2x $$ 5. **Combine like terms:** $$ (g - h)(x) = -x^3 + 2x^2 + (2x - 2x) - 3 $$ $$ (g - h)(x) = -x^3 + 2x^2 + 0 - 3 $$ $$ (g - h)(x) = -x^3 + 2x^2 - 3 $$ 6. **Final answer:** $$ \boxed{-x^3 + 2x^2 - 3} $$ This matches the first polynomial you provided except for the $4x$ term, which cancels out in the subtraction.