Factor out the greatest common factor from the terms of the polynomial 6x^3−12x^2+18x

Question

(1 point)
The GCF of the polynomial given is (__)

Answer 1

To find the greatest common factor (GCF) of the terms in the polynomial \(6x^3 - 12x^2 + 18x\), we can analyze the coefficients and the variable parts:

1. Coefficients: The coefficients are 6, -12, and 18.

   • The GCF of the numbers 6, -12, and 18 is 6.

2. Variable part: The variable terms are \(x^3\), \(x^2\), and \(x\).

   • The lowest power of \(x\) among these is \(x\).

Now we combine the GCF of the coefficients and the variable parts:

• The GCF of the polynomial \(6x^3 - 12x^2 + 18x\) is \(6x\).

Thus, the GCF of the polynomial is \( \boxed{6x} \).