Question

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

Answer 1

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

Explanation:

`F(y) = 26y^2 - 172y - 70 = 2f(y) = 2(13y^2 - 86y - 35)`
Factor f(y) by using new AC Method (Socratic Search).
Converted trinomial:
`f'(y) = y^2 - 86y - 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: `5/a = 5/13`, and
`-91/a = -91/13 = - 7`.
Factored form of F(y):
`F(y) = 2f(y) = 2(13)(y + 5/13)(y - 7) = 2(13y + 5)(y - 7)`