Question

How do you factor `6s ^ { 2} - 11s + 3`?

Answer 1

(3s - 1)(2s - 3)

Explanation:

`f(s) = 6s^2 - 11s + 3 =` 6(s + p)(s + q)
Use the new AC Method (Socratic, Google Search)
Converted trinomial:
`f'(s) = s^2 - 11s + 18`.
Find 2 numbers p' and q' knowing the sum (-b = -11) and the product (ac = 18). They are: p' = -2 and q' = - 9.
Back to original f(s), `p = (p')/a = - 2/6 = - 1/3` and
`q = (q')/a = - 9/6 = - 3/2`.
Factored form:
`f(s) = 6(s - 1/3)(s - 3/2) = (3s - 1)(2s - 3)`