Question

Solve 12x2 + x - 6 = 0 by factoring

Answer 1

for a quadratic \[ax^2 + bx + c = 0\]

multiply a and c then find the factors that add to b, you have the larger factor as positive and the smaller negative

so 12* -6 = -72

factors that add to 1 are 9 and - 8

next write the binomials in the form

(ax + factor 1)(ax + factor 2)
-------------------------- = 0
a


so you have

(12x + 9)(12x - 8)
----------------- = 0
12

by removing common factors from each binomial, you'll be able to cancel the denominator, leaving the simplified factored form of the quadratic.