Question

How do you factor `3x^2 - 10 + 3 = 0`?

Answer 1

(3x - 1)(x - 3)

Explanation:

Use the new AC Method (Socratic).
`y = 3x^2 - 10 + 3 =` 3(x + p)(x + q)
Converted `y' = x^2 - 10x + 9 =` (x + p')(x + q').
Find p' and q' knowing sum (-10) and product (9). They are: p' = -1 and q' = -9.
Back to y --> `p = (p')/a = -1/3` and `q = (q')/a = -9/3 = -3.`
Factored form y = 3(x - 1/3)(x- 3) = (3x - 1)(x - 3)