Question

How do you factor `8x^2 - 49x + 45`?

Answer 1

(8x - 9)(x - 5)

Explanation:

Use the new AC Method to factor trinomials (Google, Yahoo Search).
`y = 8x^2 - 49x + 45 =`8(x + p)(x + q)
Converted trinomial: `y' = x^2 - 49x + 360 =` (x + p')(x + q').
p' and q' have same sign because ac > 0.
Compose factor pairs of (ac = 360) --> ... (8, 45)(9, 40). This sum is
9 + 40 = 49 = -b. Then, the opposite pairs (-9, - 40) gives p' = -9 and q' = -40.
Back to original trinomial y, we get: `p = (p')/a = -9/8` and `q = (q')/a = -40/8 = -5.`
Factored form `y = 8(x - 9/8)(x - 5) = (8x- 9)(x - 5)`