How do you factor 8x^2+65x+8?

Aug 9, 2015

Factor $y = 8 {x}^{2} + 65 x + 8$

Ans: (8x + 1)(x + 8)

Explanation:

Use the new AC Method. y = 8(x - p)(x - q).
Converted trinomial$y ' = {x}^{2} + 65 x + 64 =$(x - p')(x - q').
p' and q' have same sign (a and c same sign)
Factor pairs of 64 -> (1, 64). This sum is 65 = b.
Then p' = 1 and q' = 64.
Therefor,$p = \frac{p '}{a} = \frac{1}{8}$ and $q = \frac{64}{8} = 8$

$y = 8 \left(x + \frac{1}{8}\right) \left(x + 8\right) = \left(8 x + 1\right) \left(x + 8\right)$