Question

How do you factor `3x^2 + 5x - 28`?

Answer 1

`3x^2+5x-28=(3x-7)(x+4)`

Explanation:

`3x^2+5x-28=(3x-7)(x+4)`

Answer 2

(3x - 7)(x + 4)

Explanation:

Use the new AC method to factor trinomials (Socratic Search)
`y = 3x^2 + 5x - 28 =` 3(x + p)(x + q)
`Converted trinomial y' = x^2 + 5x - 84 =` (x + p')(x + q')
p' and q' have opposite signs, because ac < 0.
Factor pairs of (ac = -84) -->...(-4, 21)(-7, 12). This sum is 5 = b. Then, p' = -7 and q' = 12.
Back to y, `p = (p')/a = -7/3` and `q = (q')/a = 12/3 = 4.`
Factored form:
`y = 3(x - 7/3)(x + 4) = (3x - 7)(x + 4)`