Question

How do you factor `3v^2+14v+8`?

Answer 1

`y = 3v^2 + 14v + 8.`= (x - p)(x - q)
I use the new AC Method to factor trinomials (Google, Yahoo Search)

Converted trinomial: `y' = v^2 + 14v + 24 =` (x -p')(x - q') (a,c = 24)
Compose factor pairs of 24: (1, 24)(2, 12). This sum is 14 = b. Then
p' = 2 and q' = 12. Back to original trinomial: `p = (p')/a = 2/3`, and `q = (q')/a = 12/3 = 4.`

Factored form: `y = (x + 2/3)(x + 4) = (3x + 2)(x + 4)`

Check by developing
`y = 3x^2 + 12x + 2x + 8) = 3x^2 + 14x + 8`. OK