Question

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

Answer 1

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

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