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

Answer 1

To find the greatest common factor (GCF) of the polynomial \( 4x^4 + 12x^3 - 36x^2 + 24x \), we can look at the coefficients and the variable parts.

1. Coefficients: The coefficients of each term are 4, 12, -36, and 24. The GCF of these coefficients is 4.
2. Variable Parts: The variables in each term are \( x^4, x^3, x^2, \) and \( x \). The lowest power of \( x \) among these is \( x^1 \) (or just \( x \)).

Combining these two parts, we see that the GCF of the polynomial is: \[ 4x \]

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