Question

How do you factor completely `5x^3 - 26x^2 + 5x`?

Answer 1

x(5x - 1)(x - 5)

Explanation:

`f(x) = xy = x(5x^2 - 26x + 5)`
Factor the trinomial y by the new AC Method (Socratic Search)
`y = 5x^2 - 26x + 5 = 5(x + p)(x + q)`
Converted trinomial: `y' = x^2 - 26x +25 =` (x + p')(x + q')
Since a + b + c = 0, then p' = -1 and q' = -25.
Back to y, `p = (p')/a = -1/5` and `q = (q')/a = -25/5 = -5.`
Factored form `y = 5(x - 1/5)(x - 5) = (5x - 1)(x - 5)`
f(x) = x(5x - 1)(x - 5)