Question: 5. g(x) = x^2 + 6x + 8
1. **State the problem:** Factor the quadratic function $$g(x) = x^2 + 6x + 8$$.
2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$.
3. Here, $$a=1$$, $$b=6$$, and $$c=8$$. We need two numbers that multiply to $$1 \times 8 = 8$$ and add to $$6$$.
4. The numbers $$2$$ and $$4$$ satisfy this because $$2 \times 4 = 8$$ and $$2 + 4 = 6$$.
5. Rewrite the middle term using these numbers:
$$x^2 + 2x + 4x + 8$$
6. Group terms:
$$(x^2 + 2x) + (4x + 8)$$
7. Factor each group:
$$x(x + 2) + 4(x + 2)$$
8. Factor out the common binomial:
$$(x + 4)(x + 2)$$
**Final answer:** $$g(x) = (x + 4)(x + 2)$$