Factor Quadratic 53Da62

1. **State the problem:** We need to factor the quadratic expression $$-3x^2 + 15x + 108$$. 2. **Formula and rules:** To factor a quadratic expression of the form $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Step 1: Factor out the greatest common factor (GCF):** The GCF of $$-3x^2$$, $$15x$$, and $$108$$ is $$-3$$. $$-3x^2 + 15x + 108 = -3(x^2 - 5x - 36)$$ 4. **Step 2: Factor the quadratic inside the parentheses:** We want two numbers that multiply to $$-36$$ and add to $$-5$$. These numbers are $$-9$$ and $$4$$ because $$-9 \times 4 = -36$$ and $$-9 + 4 = -5$$. 5. **Step 3: Write the factored form:** $$-3(x - 9)(x + 4)$$ 6. **Final answer:** The factored form of $$-3x^2 + 15x + 108$$ is $$-3(x - 9)(x + 4)$$.