1. Problem: Do a factoring example. 2. Let's factor a simple quadratic: $x^2+5x+6$. 3. Formula used for factoring trinomials: $$x^2+bx+c=(x+m)(x+n)$$ where $m+n=b$ and $mn=c$. 4. Here, we need two numbers that add to $5$ and multiply to $6$. 5. Those numbers are $2$ and $3$ because $2+3=5$ and $2\cdot 3=6$. 6. So we write: $$x^2+5x+6=(x+2)(x+3)$$ 7. Check by multiplying back: $$ (x+2)(x+3)=x^2+3x+2x+6=x^2+5x+6 $$ 8. Final answer: $x^2+5x+6=(x+2)(x+3)$.