Factor completely: 2n^2 - 8n - 42.

1. Factor out the GCF first: 2n squared - 8n - 42 has a common factor of 2, giving 2(n squared - 4n - 21). 2. Inside the parentheses, find two numbers that multiply to -21 and add to -4. 3. The pair 3 and -7 multiplies to -21 and adds to -4. 4. Use 3 and -7 as the last terms to get 2(n + 3)(n - 7), and check: 2 times (n squared - 4n - 21) gives back 2n squared - 8n - 42. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_