Question

How do you factor `7(x^2) - 19x - 6`?

Answer 1

`(7x + 2)(x - 3)`

Explanation:

`7x^2 - 19x - 6 = (7x + 2)(x - 3)`

Answer 2

Factor `y = 7x^2 - 19x - 6`

Ans: (7x + 2)(x - 3)

Explanation:

y = a(x + p)(x + q)
I use the new AC Method to factor trinomials (Socratic Search).
Converted trinomial: `y' = x^2 - 19x - 42 =` (x + p')(x + q'). p' and q' have opposite signs, Factor pairs of (-42) -->(-2, 21). This sum is 19 = -b. The opposite sum gives: p' = 2 and q' = -21.
Therefor: `p = 2/7` and `q = -21/7 = -3`.
The factored form is: `y = 7(x + 2/7)(x - 3) = (7x + 2)(x - 3)`