Factor 2x^2 + 7x + 3

Problem: Factor the quadratic expression $2x^2 + 7x + 3$.

Steps

1. Find two numbers that multiply to $2 \cdot 3 = 6$ and add up to $7$
   $$\text{The numbers are } 6 \text{ and } 1$$
2. Split the middle term using these two numbers
   $$2x^2 + 6x + x + 3$$
3. Factor by grouping
   $$2x(x + 3) + 1(x + 3)$$
4. Factor out the common binomial $(x + 3)$
   $$(2x + 1)(x + 3)$$