Question

How do you factor completely: `6x^2 + 19x + 10`?

Answer 1

Factor: y = 6x^2 + 19x + 10
y = (3x + 2)(2x + 5)

Explanation:

`y = 6x^2 + 19x + 10 =` 6(x - p)(x - q).
I use the new AC Method to factor trinomials (Google, Yahoo search)
Converted `y' = x^2 + 19x + 60 =` (x - p')(x - q'). p' and q' have same sign.
Factor pairs of ac = 60 -> ...(3, 20)(4, 15). This sum is 19 = b.
Then p' = 4 and q' = 15
Then, `p = 4/6 = 2/3` and `q = 15/6 = 5/2`

`y = 6(x + 2/3)(x + 5/2) = (3x + 2)(2x + 5)`