From the archives — Originally published on April 5th, 2005

6x² + 19x - 20

1. Multiply the first and last coefficients to get a key number:
   6 × -20 = -120
2. Factor the key number:
   -120 = -1 × 2 × 2 × 2 × 3 × 5
3. Find two factors that add up to the coefficient of the center term:
   24 = 2 × 2 × 2 × 3, -5 = -1 × 5
4. Split the center term into two terms, each using one of the previously found factors as a coefficient:
   (6x² + 24x) + (-5x - 20)
5. Factor each binomial so you have the same terms in each parentheses:
   6x(x + 4) + -5(x + 4)
6. Take out each binomial’s coefficient, making them a binomial, multiply that new binomial by the old binomial you had:
   (6x - 5)(x+4)