Question

How do you factor the trinomial `25x^2-15x+2`?

Answer 1

Factor: `y = 25x^2 - 15x + 2`

Ans: (5x - 1)(5x - 2)

Explanation:

I use the new AC Method to factor trinomials (Socratic Search)
y = 25x^2 - 15x + 2 = 25(x + p)(x + q)
Converted trinomial: y' = x^2 - 15x + 50 = (x + p')(x + q'). P' and q' have same sign. Factor pairs of (50) --> (2, 25)(5, 10). This sum is 15 = -b. Therefor, the opposite sum gives p' = -5 and q' = -10.
Back to original trinomial, p = (p')/a = -5/25 = -1/5 and q = (q')/a = -10/25 = -2/5.
Factored form: y = 25(x - 1/5)(x - 2/5) = (5x - 1)(5x - 2)