SOLUTION: Find the zeros of the function algebraically. f(x)=x^3-x^2-25x+25

Question 885669: Find the zeros of the function algebraically.
f(x)=x^3-x^2-25x+25
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f(x) = x^3 - x^2 - 25x + 25
set it equal to zero to get:
x^3 - x^2 - 25x + 25 = 0
separate into 2 parts as shown below:
(x^3 - x^2) - (25x - 25) = 0
factor out x^2 in the left part and factor out 25 in the right part to get:
x^2 * (x - 1) - 25 * (x - 1) = 0
factor out the common (x-1) term to get:
(x^2 - 25) * (x - 1) = 0
factor (x^2 - 25) to get:
(x - 5) * (x + 5) * (x - 1) = 0
those are your factors.
the zeroes are:
x = 5
x = -5
x = 1
a graph of your equation looks like this:
$$$

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