Using trial and error, factor: 6b^2 - 13b + 5.

1. Find the factors of the first term, 6b squared: 1b and 6b, or 2b and 3b. 2. Find the factors of the last term, 5: since 5 is positive and the middle term is negative, both factors of 5 must be negative, giving -1 and -5. 3. Test the combinations: (2b - 1)(3b - 5) multiplies out to 6b squared - 13b + 5, which matches the original trinomial. 4. The other combinations, such as (b - 1)(6b - 5) or (b - 5)(6b - 1), produce different middle terms and do not match. 5. Check by multiplying: 6b squared - 10b - 3b + 5 gives back 6b squared - 13b + 5. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_