Question

How do you factor the trinomial `8q^2-10q+3=0`?

Answer 1

(2q - 1)(4q - 3)

Explanation:

Use the new AC Method (Socratic Search)
`y = 8q^2 - 10q + 3 =`8(q + m)(q + n).
Converted `y' = q^2 - 10q + 24 =` (q + m')(q + n')
m' and n' have same sign (ac > 0)
Factor pairs of (ac = 24) --> (-4, -6). This sum is (-10 = b).
Then, m' = -4, and n' = -6.
Back to y, `m = (m')/a = -4/8 = -1/2`, and `n = (n')/a = -6/8 = -3/4`.
Factored form:
`y = 8(q - 1/2)(q - 3/4) = (2q - 1)(4q - 3)`