Question: User: $x^2-5x+6$
1. **State the problem:** Simplify or factor the quadratic expression $$x^2 - 5x + 6$$.
2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$.
3. **Apply to the problem:** Here, $$a=1$$, $$b=-5$$, and $$c=6$$.
4. **Find two numbers:** We need two numbers that multiply to $$1 \times 6 = 6$$ and add to $$-5$$. These numbers are $$-2$$ and $$-3$$.
5. **Write the factored form:**
$$
x^2 - 5x + 6 = (x - 2)(x - 3)
$$
6. **Verify by expansion:**
$$
(x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6
$$
**Final answer:** $$ (x - 2)(x - 3) $$