Question

How do you factor `y= 6x^2 + 11x + 4` ?

Answer 1

`y=(2x+1)(3x+4)`

Explanation:

`y=6x^2+11x+4`

`y=(2x+1)(3x+4)`

Answer 2

y = (2x + 1)(3x + 4)

Explanation:

Use the new AC Method (Socratic Search)
`y = 6x^2 + 11x + 4 =` 6(x + p)(x + q)
Converted trinomial: `y' = x^2 + 11x + 24 =` (x + p')(x + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 24) --> ...(2, 12)(3, 8). This sum is 11 = b. Then, p' 3 and q' = 8.
Back to the original y --> `p = (p')/a = 3/6 = 1/2`, and
`q = (q')/a = 8/6 = 4/3`
Factored form: `y = 6(x + 1/2)(x + 4/3) = (2x + 1)(3x + 4)`