Question

How do you factor `16b^2+60b-100`?

Answer 1

I use the new AC Method (Google, Yahoo Search)
`f(x) = 4(4x^2 + 15x - 25) =`4(x - p)(x - q)

Converted function: f'(x) = 4(x^2 + 15x - 100) = 4(x - p')(x - q')
Factor pairs of (-100): (-2, 50)(-4, 25)(-5, 20). This last sum is 15 = b.
Then p' = -5 and q' = 20
Then,`p= (p')/a = -5/4`and `q = (q')/a = 20/4 = 5`

Factored form of f(x) :
`f(x) = 4(x - 5/4)(x + 5) =4 (4x - 5)(x + 5)`

Check by developing:`f(x) = 4(4x^2 + 20x - 5x - 25).` OK