Using trial and error, factor: 14x^2 - 47x - 7.

1. The factors of 14x squared are x and 14x, or 2x and 7x. 2. The last term is -7, which is negative, so its factors must have opposite signs: 1 and -7, or -1 and 7. 3. Testing the combination (2x - 7)(7x + 1), the outer and inner terms are 2x and -49x, which combine to -47x, matching the middle term. 4. Check by multiplying: 14x squared + 2x - 49x - 7 gives back 14x squared - 47x - 7. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_