Factor: q^2 - 2q - 15.

1. Write the factors as two binomials with first terms q. 2. List factor pairs of -15 and their sums: 1,-15 sums to -14; -1,15 sums to 14; 3,-5 sums to -2; -3,5 sums to 2. 3. The pair 3 and -5 multiplies to -15 and adds to -2, matching the middle term. 4. Use 3 and -5 as the last terms to get (q + 3)(q - 5). 5. Check by multiplying: q squared - 5q + 3q - 15 gives back q squared - 2q - 15. 6. The pair -3 and 5 also multiplies to -15 but adds to positive 2, which is the wrong sign for this trinomial's middle term. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.2 Factor Quadratic Trinomials with Leading Coefficient 1_