Question

How do you factor `10x^2+23x+6`?

Answer 1

(10x + 3)(x + 2)

Explanation:

Use the new systematic, non-guessing AC Method (Socratic Search)
`y = 10x^2 + 23x + 6 =` 10(x + p)(x + q)
Converted trinomial: `y' = x^2 + 23x + 60 =`(x + p')(x + q').
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 60) --> (2, 30)(3, 20). This last sum is 23 = b.
Then, `p = (p')/a = 3/10` and `q = (q')/a = 20/10 = 2`

Factored form: `y = 10(x + 3/10)(x + 2) = (10x + 3)(x + 2)`