Question

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

Answer 1

(2x - y)(x - 5y)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
`y = 2x^2 - 11xy + 5y^2 =` 2(x + p)(x + q)
Converted trinomial: `y' = x^2 - 11xy + 10y^2 =` (x + p')(x + q')
p' and q' have same sign because ac > 0
Factor pairs of `(ac = 10y^2)` --> (-y, -10y). This sum is (-11y = b). Consequently, p' = -y and q' = -10y.
Back to original trinomial y --> `p = (p')/a = -y/2`, and `q = (q')/a = -10y/2 = -5y.`
Factored form of y:
`y = 2(x - y/2)(x - 5y) = (2x - y)(x - 5y)`