1. **State the problem:** Factor the quadratic expression $2x^2 + 7x + 3$ as a trinomial where the leading coefficient is not 1. 2. **Recall the factoring method:** For a quadratic $ax^2 + bx + c$ where $a \neq 1$, find two numbers that multiply to $a \times c$ and add to $b$. 3. **Calculate the product and sum:** Here, $a = 2$, $b = 7$, $c = 3$. So, $a \times c = 2 \times 3 = 6$. 4. **Find two numbers that multiply to 6 and add to 7:** These numbers are 6 and 1. 5. **Rewrite the middle term using these numbers:** $$2x^2 + 6x + 1x + 3$$ 6. **Group terms:** $$(2x^2 + 6x) + (1x + 3)$$ 7. **Factor each group:** $$2x(x + 3) + 1(x + 3)$$ 8. **Factor out the common binomial:** $$(2x + 1)(x + 3)$$ **Final answer:** $$2x^2 + 7x + 3 = (2x + 1)(x + 3)$$