Question

How do you factor completely `8c^2 - 26c + 15`?

Answer 1

y = (4x - 3)(2x - 5)

Explanation:

Use the new AC Method (Socratic Search)
`y = 8c^2 - 26c + 15 =` 8(x + p)(x + q)
Converted trinomial: `y' = c^2 - 26c + 120 =`(x + p')(x + q').
p' and q' are both negative (Rule of Signs)
Factor pairs of (120) -->...(-5, - 24)(-6, -20). This sum is (-26 = b).
Then, p' = -6 and q' = -20.
Back to y, `p = (p')/a = -6/8 = -3/4`, and `q = (q')/a = -20/8 = - 5/2`
`y = 8(x - 3/4)(x - 5/2) = (4x - 3)(2x - 5)`