# How do you factor 7x^2-30x+8?

Aug 8, 2015

Factor: $y = 7 {x}^{2} - 30 x + 8$

Ans: (7x - 2)(x - 4)

#### Explanation:

I use the new AC Method: y = 7(x - p)(x - q)
Converted trinomial $y ' = {x}^{2} _ 30 x + 56 =$(x - p')(x - q')
p' and q' have same sign (Rule of signs)
Factor pairs of 56 --> (2, 28). This sum is 30 = -b.
Change this sum to the opposite. Then p' = -2 and q' = -28.
Therefor, p = (p')/a = -2/7 and q' = -28/7 = -4

y = 7(x - 2/7)(x - 4) = (7x - 2)(x - 4)