Find the zeros of f(x) = x^3 - 5x^2 - x +5 by factoring

Answer 1

To find the zeros of the function f(x) = x^3 - 5x^2 - x + 5 by factoring, we need to find the values of x that make the function equal to zero.

We start by factoring out the common factor, which is 1:

f(x) = x^3 - 5x^2 - x + 5
= (x^3 - 5x^2) - (x - 5)
= x^2(x - 5) - (x - 5)
= (x - 5)(x^2 - 1)

Now we have a difference of squares, which can be factored further:

f(x) = (x - 5)(x - 1)(x + 1)

To find the zeros, we set each factor equal to zero and solve for x:

x - 5 = 0 -> x = 5
x - 1 = 0 -> x = 1
x + 1 = 0 -> x = -1

Therefore, the zeros of f(x) = x^3 - 5x^2 - x + 5 are x = 5, x = 1, and x = -1.