1. The problem is to simplify the sum of the expressions $x^2 - 8x + 5$ and $-3x^2 + 5x - 9$ by collecting like terms. 2. Write the sum explicitly: $$ (x^2 - 8x + 5) + (-3x^2 + 5x - 9) $$ 3. Combine like terms: - Combine $x^2$ terms: $x^2 + (-3x^2) = \cancel{x^2} - 3\cancel{x^2} = -2x^2$ - Combine $x$ terms: $-8x + 5x = \cancel{-8x} + 5\cancel{x} = -3x$ - Combine constants: $5 + (-9) = \cancel{5} - 9 = -4$ 4. The simplified expression is: $$ -2x^2 - 3x - 4 $$ Final answer: $-2x^2 - 3x - 4$