Question

How do you factor `7p^2 + 51p + 14`?

Answer 1

`f(x) = 7x^2 + 51x + 14` = (x - p)(x - q). Use the new AC Method.

Converted trinomial: `y' = x^2 + 51x + 98` = (x - p')(x - q').
Find p' and q' by composing factor of a.c = 98 -> (2, 49). This sum is 51 = b. Then p' = 2 and q' = 49.
Then, `p = (p')/a = 2/7`, and `q = (q')/a = 49/7 = 7.`

Factored form: y = (x + 2/7)(x + 7) = (7x + 2)(x + 7)

Check by developing: `y = 7x^2 + 49x + 2x + 14`.. OK