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

1 Answer
Nghi N.
May 12, 2016

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)

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