Question

How do you factor the expression `2x^2 + 13xy +15y^2`?

Answer 1

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

Explanation:

Consider y as a constant. factor the quadratic trinomial for x.
Use the new AC Method to factor trinomial.
`f(x) = 2x^2 + 13xy + 15y^2 =` 2(x + p)(x + q)
Converted trinomial `f'(x) = x^2 + 13xy + 30y^2 =` (x + p')(x + q')
p' and q' have same sign because ac > 0.
Factor pairs of `(ac = 30y^2)` --> (2y, 15y)(3y, 10y) . This sum is
13y = b. Then, p' = 3y and q' = 10y.
Back to original trinomial: `p = (p')/a = (3y)/2`, and
`q = (q')/a = 10y/2 = 5y.`
Factored form:
`y = 2(x + 3y/2)(x + 5y) = (2x + 3y)(x + 5y)`