Question

How do you factor the trinomial `4a^2-16ab+15b^2`?

Answer 1

(2a - 3)(2a - 5)

Explanation:

Consider a as an variable, b as a constant, and factor the trinomial, using the new AC Method (Socratic Search).
`y = 4a^2 - 16ab + 15b^2 =` 4(a + p)(a + q)
Converted trinomial `y' = a^2 - 16ab + 60b^2 =` (a + p')(a + q')
p' and q' have same sign because ac > 0.
Factor pairs of `(ac = 60b^2)`--> (-6b, -10b). This sum is -16b = b. Then p' = -6b and q' = -10b.
Back to original trinomial y, `p = (p')/a = -6b/4 = -(3b)/2` and
`q = (q')/a = -(10b)/4 = (-5b)/2.`
Factored form : `y = 4(a - (3b)/2)(a - (5b)/2) = (2a - 3b)(2a - 5b)`