Question

How do you factor `5x^2-11x+2`?

Answer 1

Factor y = 5x^2 - 11x + 2.

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

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
`y = 5x^2 - 11x + 2 =` 5(x + p)(x + q)
Converted trinomial:
`y' = x^2 - 11x + 10 =` (x + p')( x = q').
Find p' and q' knowing sum (b = - 11) and product (ac = 10).
They are: p' = -1, and q' = -10
Therefor: `p = (p')/a = -1/5`, and q = (q')/a = -10/5 = -2
Factored form of y:
`y = 5(x - 1/5)(x - 2) = (5x - 1)(x - 2)`