1. The problem is to simplify or understand the expression $x^3 - x^2 + x_1$. 2. Note that $x_1$ typically denotes a variable or a subscripted variable, different from $x$. If $x_1$ is a separate variable, the expression is already simplified. 3. If you meant $x^3 - x^2 + x$, then the expression is a cubic polynomial. 4. To factor $x^3 - x^2 + x$, factor out the common term $x$: $$x^3 - x^2 + x = x(x^2 - x + 1)$$ 5. The quadratic $x^2 - x + 1$ does not factor further over the real numbers because its discriminant is $(-1)^2 - 4 \times 1 \times 1 = 1 - 4 = -3 < 0$. 6. Therefore, the fully factored form over the reals is: $$x(x^2 - x + 1)$$ 7. If $x_1$ is a separate variable, the expression remains as $x^3 - x^2 + x_1$ with no further simplification. Final answer depends on interpretation: - If $x_1$ is a separate variable, expression is $x^3 - x^2 + x_1$. - If $x_1$ was a typo for $x$, then factored form is $x(x^2 - x + 1)$.