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w³ + 5w² - w = 5
Get 0 on the right by adding -5 to both sides:
w³ + 5w² - w - 5 = 0
Factor w² out of the first two terms on the
left and factor -1 out of the last two.
w²(w + 5) - 1(w + 5) = 0
Factor (w + 5) out of both terms:
(w + 5)(w² - 1) = 0
Factor the second factor as the difference
of two squares:
(w + 5)(w - 1)(w + 1) = 0
Set each factor = 0.
Setting w + 5 = 0 gives w = -5
Setting w - 1 = 0 gives w = 1
Setting w + 1 = 0 gives w = -1
The three solutions are -5, 1, and -1
Edwin
