which of the following is the gcf of the polynomial 4x^4+12x^3-36x^2+24x

Answer 1

To find the greatest common factor (GCF) of the polynomial \( 4x^4 + 12x^3 - 36x^2 + 24x \), we can follow these steps:

1. Factor out the coefficients: Start by examining the numerical coefficients \( 4, 12, -36, \) and \( 24 \).

   • The GCF of these numbers is \( 4 \).

2. Factor out the variable part: Next, look at the variable \( x \):

   • The smallest power of \( x \) present in all terms is \( x \) (since the lowest degree term is \( x^1 \)).

3. Combine the GCFs: Therefore, the GCF of the polynomial is \( 4x \).

Now, let's confirm this by factoring \( 4x \) out of the polynomial:

\[ 4x^4 + 12x^3 - 36x^2 + 24x = 4x(x^3 + 3x^2 - 9x + 6) \]

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