Find all zeros of the function g (x) = x^3-x^2-x+1

The zeroes of this equation would be - 1 and a double root at 1.

Step-by-step explanation:

To find these, start factoring by splitting. In this, we first only look at the first two terms. Then we pull out the greatest common factor.

x^3 - x^2

x^2 (x - 1)

Now we do the same with the next two numbers.

-x + 1

-1 (x - 1)

Now we can use the things outside the parenthesis along with the common parenthesis as the factors.

(x^2 - 1) (x - 1)

And we can factor the first parenthesis by using the difference of two squares model.

(x + 1) (x - 1) (x - 1)

And finally, we can find the zeroes by setting each parenthesis equal to 0.

x + 1 = 0

x = - 1

x - 1 = 0

x = 1

x - 1 = 0

x = 1