Question

How do you factor the expression `4x^2 - 8x - 5`?

Answer 1

This expression can be factor by playing with factors of `4` and factors of `5` giving:

`(2x - 5)(2x + 1)`

Answer 2

y = (2x + 1)(2x - 5)

Explanation:

Use the new AC Method to factor trinomial (Socratic Search)
`y = 4x^2 - 8x - 5 = 4(x + p)(x + q)`
Converted trinomial:
`y' = x^2 - 8x - 20 = (x + p')(x + q')`
Proceeding: find p' and q', then divide them by (a = 4) to find p and q.
Find 2 numbers p' and q' knowing sum (b = -8), and product (ac = -20). They are p' = 2 and q' = -10.
Therefor: `p = (p')/a = 2/4 = 1/2` and `q = - 10/4 = - 5/2`.
Factored form:
`y = 4( x + 1/2)(x - 5/2) = (2x + 1)(2x - 5)`