Factorise Quadratic 240588

1. **State the problem:** Factorise the quadratic expression $$x^2 + 5x + 6$$. 2. **Recall the formula:** To factorise a quadratic of the form $$x^2 + bx + c$$, find two numbers that multiply to $$c$$ and add to $$b$$. 3. **Identify values:** Here, $$b = 5$$ and $$c = 6$$. 4. **Find factors:** The pairs of numbers that multiply to $$6$$ are: - $$1 \times 6 = 6$$ (sum $$7$$) - $$2 \times 3 = 6$$ (sum $$5$$) 5. **Select correct pair:** Since $$2 + 3 = 5$$, the correct pair is $$2$$ and $$3$$. 6. **Write factorised form:** $$x^2 + 5x + 6 = (x + 2)(x + 3)$$. 7. **Verification:** Expanding: $$ (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 $$, which matches the original expression. **Final answer:** $$\boxed{(x + 2)(x + 3)}$$