Find the roots of the function \(f(x) = x^3 - 9x^2 + 23x - 15\) using the factor theorem.

Step 1 ：The factor theorem states that a polynomial \(f(x)\) has a factor \((x - k)\) if and only if \(f(k) = 0\). So we first need to find a value of \(x\) that makes \(f(x) = 0\).

Step 2 ：By trying a few values, we find that \(f(1) = 1^3 - 9 * 1^2 + 23 * 1 - 15 = 0\), so \((x - 1)\) is a factor of \(f(x)\).

Step 3 ：Next, we can perform polynomial division to divide \(f(x)\) by \((x - 1)\) to find the other factors. The result is \(x^2 - 8x + 15\), which can be factored into \((x - 3)(x - 5)\).

Step 4 ：Therefore, the factors of \(f(x)\) are \((x - 1)(x - 3)(x - 5)\), and the roots of the function are \(x = 1\), \(x = 3\), and \(x = 5\).