Split The Middle Term
LittleZephyr: Wednesday, February 9th, 20056x2 + 19x - 20
- Multiply the first and last coefficients to get a key number:
6 × -20 = -120 - Factor the key number:
-120 = -1 × 2 × 2 × 2 × 3 × 5 - Find two factors that add up to the coefficient of the center term:
24 = 2 × 2 × 2 × 3, -5 = -1 × 5 - Split the center term into two terms, each using one of the previously found factors as a coefficient:
(6x2 + 24x) + (-5x - 20) - Factor each binomial so you have the same terms in each parentheses:
6x(x + 4) + -5(x + 4) - Take out each binomial’s coefficient, making them a binomial, multiply that new binomial by the old binomial you had:
(6x - 5)(x+4)

