Question

How do you factor `6x^2+25x+25`?

Answer 1

(3x + 5)(2x + 5)

Explanation:

Use the new AC Method (Socratic Search)
`y = 6x^2 + 25x + 25) =` 6(x + p)(x + q).
Converted trinomial `y' = x^2 + 25x + 150 =` (x + p')(x + q').
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 150) --> (10, 15). This sum is 25 = b. Then, p' = 10 and q' = 15.
Back to original y, `p = (p')/a = 10/6 = 5/3`, and `q = (q')/a = 15/6 = 5/2`.
Factored form `y = 6(x + 5/3)(x + 5/2) = (3x + 5)(2x + 5)`