Factor Trinomial Ae8610

1. **State the problem:** Factor the trinomial $$2x^2 + 5x + 3$$. 2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Calculate the product and sum:** Here, $$a = 2$$, $$b = 5$$, and $$c = 3$$. - Product: $$2 \times 3 = 6$$ - Sum: $$5$$ 4. **Find two numbers that multiply to 6 and add to 5:** These numbers are $$2$$ and $$3$$. 5. **Rewrite the middle term using these numbers:** $$2x^2 + 2x + 3x + 3$$ 6. **Group terms:** $$(2x^2 + 2x) + (3x + 3)$$ 7. **Factor each group:** $$2x(x + 1) + 3(x + 1)$$ 8. **Factor out the common binomial:** $$(2x + 3)(x + 1)$$ **Final answer:** $$\boxed{(2x + 3)(x + 1)}$$