1. **State the problem:** Subtract the polynomials $\left(5x^2 - 9x + 4\right)$ and $\left(-x^2 + 6x + 2\right)$. That is, find $$\left(5x^2 - 9x + 4\right) - \left(-x^2 + 6x + 2\right).$$ 2. **Write the subtraction explicitly:** $$5x^2 - 9x + 4 - \left(-x^2 + 6x + 2\right).$$ 3. **Distribute the minus sign:** $$5x^2 - 9x + 4 + x^2 - 6x - 2.$$ 4. **Combine like terms:** - Combine $x^2$ terms: $$5x^2 + x^2 = 6x^2.$$ - Combine $x$ terms: $$-9x - 6x = -15x.$$ - Combine constants: $$4 - 2 = 2.$$ 5. **Final simplified expression:** $$6x^2 - 15x + 2.$$ 6. **Explanation:** When subtracting polynomials, distribute the negative sign to each term inside the second parentheses, then combine like terms by adding coefficients of the same powers of $x$. **Answer:** $$6x^2 - 15x + 2.$$