Factor completely. 6z3 – 27z2 + 12z
State which method should be applied as the first step for factoring the polynomial.
To factor the polynomial 6z^3 – 27z^2 + 12z, we can start by finding the greatest common factor (GCF) of the terms.
The GCF of 6z^3, -27z^2, and 12z is 3z. Therefore, we can factor out 3z from each term:
3z(2z^2 – 9z + 4)
Now we have a quadratic expression inside the parentheses. To further factor this quadratic expression, we can use factoring by grouping or the quadratic formula, depending on the nature of the expression.
If it is factorable, we can use factoring by grouping to find the remaining factors. If not, we can use the quadratic formula to find the roots and rewrite the expression using these roots as factors.
So the first step is to factor out the greatest common factor: 3z.