Question: b) $x^2 - 9x + 18$
1. **State the problem:**
We need to factor the quadratic expression $$x^2 - 9x + 18$$.
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. **Identify coefficients:**
Here, $$a = 1$$, $$b = -9$$, and $$c = 18$$.
4. **Find two numbers:**
We want two numbers that multiply to $$1 \times 18 = 18$$ and add to $$-9$$.
These numbers are $$-6$$ and $$-3$$ because $$-6 \times -3 = 18$$ and $$-6 + (-3) = -9$$.
5. **Rewrite the middle term:**
$$x^2 - 6x - 3x + 18$$
6. **Group terms:**
$$(x^2 - 6x) + (-3x + 18)$$
7. **Factor each group:**
$$x(x - 6) - 3(x - 6)$$
8. **Factor out the common binomial:**
$$(x - 3)(x - 6)$$
**Final answer:**
$$x^2 - 9x + 18 = (x - 3)(x - 6)$$