# What would a name of a binomial factor of: 26y^2-172y-70 be ?

May 15, 2018

2(13y + 5)(y - 7)

#### Explanation:

$F \left(y\right) = 26 {y}^{2} - 172 y - 70 = 2 f \left(y\right) = 2 \left(13 {y}^{2} - 86 y - 35\right)$
Factor f(y) by using new AC Method (Socratic Search).
Converted trinomial:
$f ' \left(y\right) = {y}^{2} - 86 y - 455$ --> ac = (13*(- 35) = - 455
Proceeding: Find the factor numbers of f'(x), then, divide them by
a = 13.
Find 2 numbers, that have opposite signs ac < 0, knowing the sum (b = - 86) and the product (ac = - 455). They are 5 and - 91
The factor numbers of f(y) are: $\frac{5}{a} = \frac{5}{13}$, and
$- \frac{91}{a} = - \frac{91}{13} = - 7$.
Factored form of F(y):
$F \left(y\right) = 2 f \left(y\right) = 2 \left(13\right) \left(y + \frac{5}{13}\right) \left(y - 7\right) = 2 \left(13 y + 5\right) \left(y - 7\right)$