Question

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

Answer 1

Factor: `y = 8x^2 - 30x + 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 - 30x + 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 = (p')/a = -10/8 = -5/4` and `q = -20/8 = -5/2`

`y = 8(x - 5/4)(x - 5/2) = (4x - 5)(2x - 5)`