Factor the polynomial \(12x^3 - 36x^2 + 24x\)

Step 1 ：Step 1: Identify the common factors of the coefficients of \(12x^3\), \(-36x^2\), and \(24x\). The common factor is 12x.

Step 2 ：Step 2: Factor out the common factor from each term in the polynomial: \(12x(x^2 - 3x + 2)\).

Step 3 ：Step 3: Further factor the quadratic expression \(x^2 - 3x + 2\). The factors of \(x^2 - 3x + 2\) are \((x-1)(x-2)\).

Step 4 ：Step 4: Substitute the factors into the expression to get the final factored form of the polynomial: \(12x(x - 1)(x - 2)\).