Using trial and error, factor: 3x^2 + 5x + 2.

1. The first terms of the binomials must multiply to 3x squared, so use x and 3x. 2. The last terms must multiply to 2, and since all terms in the trinomial are positive, both factors of 2 are positive: 1 and 2. 3. Testing the placement, x times 2 plus 3x times 1 gives the outer and inner terms 2x and 3x, which add to 5x, matching the middle term. 4. Use this placement to get (x + 1)(3x + 2), and check by FOIL: 3x squared + 2x + 3x + 2 gives back 3x squared + 5x + 2. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_