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There are two methods.

Factoring with FOIL (AKA Guess-and-check).

Examples:

1. 3x^{ 2} - 14x - 5

Note that there are four possibilities. And it’s rather
time consuming to have to FOIL each time to find out if you have
the right answer or not.

2. 4x^{ 2} + 13x - 12

This one’s a real pain since there are, in fact, 12
possibilities.

The Grouping Method (AKA The ac-method).

Example:

4x^{ 2} + 13x - 12

There’s still an aspect of guess-and-check here, but it
involves integers rather than binomials and the check is simply
addition. I find it much easier, myself.