Factor Quadratic D9B20E

1. **State the problem:** Factor the quadratic expression $$X^2 - x - 12$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, find two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -1$$, and $$c = -12$$. 4. **Find two numbers:** We need two numbers that multiply to $$1 \times (-12) = -12$$ and add to $$-1$$. 5. **Possible pairs:** $$-4$$ and $$3$$ because $$-4 \times 3 = -12$$ and $$-4 + 3 = -1$$. 6. **Rewrite the middle term:** $$X^2 - 4X + 3X - 12$$. 7. **Group terms:** $$(X^2 - 4X) + (3X - 12)$$. 8. **Factor each group:** $$X(X - 4) + 3(X - 4)$$. 9. **Factor out common binomial:** $$(X - 4)(X + 3)$$. 10. **Final answer:** The factored form of $$X^2 - x - 12$$ is $$(X - 4)(X + 3)$$.