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

1 Answer
Mar 27, 2016

Answer:

(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)