## Problem: Factor $x^2+5x+6$. 1. **Use the factoring (AC) method for $x^2+bx+c$**. 2. Identify $b=5$ and $c=6$. 3. Compute $b\cdot c=5\cdot 6=30$. 4. Find two numbers that multiply to $30$ and add to $5$. 5. The numbers are $2$ and $3$ because $2\cdot 3=6$ and $2+3=5$. 6. Rewrite the middle term using those numbers: $$x^2+5x+6=x^2+2x+3x+6$$ 7. Factor by grouping: $$x^2+2x+3x+6=(x^2+2x)+(3x+6)$$ 8. Factor each group: $$x^2+2x=x(x+2)$$ $$3x+6=3(x+2)$$ 9. Put the common factor together: $$x(x+2)+3(x+2)=(x+2)(x+3)$$ 10. **Final answer:** $\boxed{(x+2)(x+3)}$.