Questions: Find all zeros of f(x)=x^3+x^2+x+1. Enter the zeros separated by commas.

Solution Steps

The given polynomial is $f(x) = x^3 + x^2 + x + 1$.

To find the zeros, we need to factor the polynomial. Notice that $f(x)$ can be factored by grouping: $$f(x) = x^3 + x^2 + x + 1 = (x^3 + x^2) + (x + 1)$$ $$f(x) = x^2(x + 1) + 1(x + 1)$$ $$f(x) = (x^2 + 1)(x + 1)$$

Set each factor equal to zero and solve for $x$:

1. $x^2 + 1 = 0$ $$x^2 = -1$$ $$x = \pm i$$ (where $i$ is the imaginary unit)

2. $x + 1 = 0$ $$x = -1$$

Final Answer