Question

How do you factor `3x^2+8x=3`?

Answer 1

Factor `y = 3x^2 + 8x - 3`

Ans: y = (3x - 1)(x + 3)

Explanation:

I use the new AC Method (Socratic Search).
Converted trinomial: y' = x^2 + 8x - 9.
Factor pairs of (-9) --> (-1, 9). This sum is 8 = b. Then p' = -1 and q' = 9.
Therefor, p = -1/3 ans q = 9/3 = 3
Factored form: y = 3(x - 1/3)( x + 3) = (3x - 1)(x + 3).

NOTE . This new AC Method shows a systematic way to find the 2 numbers p and q, instead of guessing. This method also avoids the lengthy factoring by grouping.