Question

How do you factor `42c^2-29c-5`?

Answer 1

Factor `y = 42x^2 - 29x - 5`

Explanation:

`y = 42x^2 - 29x - 5 =` a(x - p)(x - q).
I use the new AC Method to factor trinomials (Google, Yahoo Search).
Converted `y' = x^2 - 29x - 210 =`(x - p')(x - q').
a and c have different signs.
Factor pairs of ac = -210 ->...(-5, 42)(-6, 35). This sum is 29 = -b.
Then p' = 6 and q' = -35.
Then, `p = (p')/a = 6/42 = 1/7` and `q = (q')/a = -35/42 = -5/6`

Factored form: `y = 42(x + 1/7)(x - 5/6) = (7x + 1)(6x - 5)`

Note. This new method is fast, systematic, no factoring by grouping and no solving binomials.