Answer:
-1, 1, 5
Step-by-step explanation:
Factor by grouping:
Factor out x² from the first two terms:
f(x) = x³ - 5x² - x + 5
f(x) = x²(x - 5) - x + 5
Factor out -1 from the last two terms:
f(x) = x²(x - 5) -1(x - 5)
Then, put the two terms together:
f(x) = (x² - 1)(x - 5)
(x² - 1) is a difference of squares that can be factored further:
f(x) = (x + 1)(x - 1)(x - 5)
Set this equal to 0, and set each factor equal to zero. Then, solve for x:
x + 1 = 0
x = -1
x - 1 = 0
x = 1
x - 5 = 0
x = 5
So, the zeroes are -1, 1, and 5
