Question: Write the following expression in factored form.
$x^2 - 10x + 16$
$(x - 8)(x + 2)$
$(x - 16)(x - 1)$
$(x - 8)(x - 2)$
$(x - 16)(x + 1)$
1. **State the problem:** Factor the quadratic expression $$x^2 - 10x + 16$$ into the product of two binomials.
2. **Recall the factoring formula:** For a quadratic expression $$x^2 + bx + c$$, we look for two numbers that multiply to $$c$$ and add to $$b$$.
3. **Identify coefficients:** Here, $$b = -10$$ and $$c = 16$$.
4. **Find two numbers:** We need two numbers whose product is $$16$$ and sum is $$-10$$.
5. **List factor pairs of 16:**
- $$1 imes 16 = 16$$ (sum $$1 + 16 = 17$$ or $$-1 + -16 = -17$$)
- $$2 imes 8 = 16$$ (sum $$2 + 8 = 10$$ or $$-2 + -8 = -10$$)
6. **Choose correct pair:** The pair $$-2$$ and $$-8$$ multiply to $$16$$ and add to $$-10$$.
7. **Write factored form:**
$$
x^2 - 10x + 16 = (x - 2)(x - 8)
$$
8. **Check options:** The option matching this is $(x - 8)(x - 2)$.
**Final answer:** $(x - 8)(x - 2)$