# How do you factor 8x^2-30x+25?

Aug 8, 2015

Factor: $y = 8 {x}^{2} - 30 x + 25$

Ans: (4x - 5)(2x - 5)

#### Explanation:

Use the new AC Method. Factored form: y = 8(x + p)(x + q)
Converted trinomial: $y ' = {x}^{2} - 30 x + 200.$
Find 2 numbers p' and q' knowing sum (b = -30) and product (ac = 200). p' and q' have same sign (Rule of signs)
Factor pairs of 200 --> (5, 10)(10,20). This sum is 30 = -b.
Change this sum to the opposite. Then p' = -10 and q' = -20
Therefor, $p = \frac{p '}{a} = - \frac{10}{8} = - \frac{5}{4}$ and $q = - \frac{20}{8} = - \frac{5}{2}$

$y = 8 \left(x - \frac{5}{4}\right) \left(x - \frac{5}{2}\right) = \left(4 x - 5\right) \left(2 x - 5\right)$