Factor out the greatest common factor (GCF) from the polynomial \(12x^3 - 36x^2 + 24x\).
Answer
Finally, write down the polynomial with the GCF factored out. The factored form of the polynomial is \(12x(x^2 - 3x + 2)\).
Step 1 ：First, find out the GCF of the coefficients and the variables separately. The GCF of the coefficients 12, 36, and 24 is 12. The GCF of the variables \(x^3\), \(x^2\), and \(x\), which are the powers of x, is \(x\).
Step 2 ：So, the GCF of the polynomial \(12x^3 - 36x^2 + 24x\) is \(12x\).
Step 3 ：Then, divide each term of the polynomial by the GCF. We get \(12x^3 / 12x = x^2\), \(-36x^2 / 12x = -3x\), and \(24x / 12x = 2\).
Step 4 ：Finally, write down the polynomial with the GCF factored out. The factored form of the polynomial is \(12x(x^2 - 3x + 2)\).
