Which of the following is the GCF of the polynomial 4x4+12x3−36x2+24x?(1 point) Responses 2x 2 x 4 4 6x 6 x 4x

Answer 1

To find the greatest common factor (GCF) of the polynomial \(4x^4 + 12x^3 - 36x^2 + 24x\), we can start by factoring out the common terms.

1. Identify the GCF of the coefficients:

   • The coefficients are 4, 12, -36, and 24.
   • The GCF of these numbers is 4.

2. Identify the GCF of the variable terms:

   • The polynomial has \(x^4\), \(x^3\), \(x^2\), and \(x\).
   • The GCF of the variable terms is \(x\) (the lowest power of \(x\)).

Now, we can combine the GCF of the coefficients and the variable terms:

\[ \text{GCF} = 4x \]

Thus, the GCF of the given polynomial \(4x^4 + 12x^3 - 36x^2 + 24x\) is 4x.

Among the options provided, it seems that 4x is not directly listed, which could be a typographical error in the options.

However, the found GCF is 4x.