1. The problem is to factor the trinomial $2x^2 + 13x + 6$. 2. We use the factoring method for trinomials of the form $ax^2 + bx + c$. 3. First, multiply $a$ and $c$: $$2 \times 6 = 12$$ 4. Find two numbers that multiply to 12 and add to $b=13$. These numbers are 12 and 1. 5. Rewrite the middle term using these numbers: $$2x^2 + 12x + 1x + 6$$ 6. Group terms: $$(2x^2 + 12x) + (1x + 6)$$ 7. Factor each group: $$2x(x + 6) + 1(x + 6)$$ 8. Factor out the common binomial: $$(2x + 1)(x + 6)$$ 9. So, the factors of $2x^2 + 13x + 6$ are $2x + 1$ and $x + 6$. 10. Checking the options, the correct factors are: - $2x + 1$ - $x + 6$