1. **State the problem:** We are given the quadratic expression $2h^2 + 5h + 3$ and asked to analyze it. 2. **Identify the type of expression:** This is a quadratic polynomial in the variable $h$. 3. **Formula for factoring quadratics:** To factor a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $a \times c$ and add to $b$. 4. **Calculate product and sum:** Here, $a=2$, $b=5$, and $c=3$. The product is $2 \times 3 = 6$ and the sum is $5$. 5. **Find two numbers:** The numbers that multiply to $6$ and add to $5$ are $2$ and $3$. 6. **Rewrite the middle term:** $2h^2 + 2h + 3h + 3$ 7. **Group terms:** $(2h^2 + 2h) + (3h + 3)$ 8. **Factor each group:** $2h(h + 1) + 3(h + 1)$ 9. **Factor out common binomial:** $(2h + 3)(h + 1)$ 10. **Final factored form:** $$2h^2 + 5h + 3 = (2h + 3)(h + 1)$$ This shows the quadratic expression factored into two binomials.