X^3+x^2+x+1

The expression \(x^3 + x^2 + x + 1\) can be factored. We can factor it by grouping the terms: \[ x^3 + x^2 + x + 1 = (x^3 + 1) + (x^2 + 1) \] However, instead, a more straightforward approach involves rewriting the expression. Notice that we can group it as follows: \[ x^3 + x^2 + x + 1 = x^2(x + 1) + 1(x + 1) = (x^2 + 1)(x + 1) \] So, the factored form of \(x^3 + x^2 + x + 1\) is: \[ (x^2 + 1)(x + 1) \] If you need to find the roots of this polynomial, you can set it equal to zero: \[ (x^2 + 1)(x + 1) = 0 \] This gives us: 1. \(x + 1 = 0 \implies x = -1\) 2. \(x^2 + 1 = 0\) has roots \(x = i\) and \(x = -i\) (complex roots). Thus, the roots of the polynomial \(x^3 + x^2 + x + 1\) are \(x = -1, i, -i\).