gcf 4x^4+12x^3-36x^2+24x

1 answer

To find the greatest common factor (GCF) of the expression \( 4x^4 + 12x^3 - 36x^2 + 24x \), we'll first look for the GCF of the coefficients and the smallest power of \( x \) in each term.

  1. Identify the coefficients: The coefficients of the terms are 4, 12, -36, and 24.

    • The GCF of these coefficients is 4.
  2. Identify the powers of \( x \): The terms have the following powers of \( x \):

    • \( x^4 \), \( x^3 \), \( x^2 \), \( x^1 \).
    • The smallest power of \( x \) is \( x^1 \).

Now, we can conclude that the GCF of the entire expression is \( 4x \).

  1. Factor out the GCF: \[ 4x^4 + 12x^3 - 36x^2 + 24x = 4x(x^3 + 3x^2 - 9x + 6). \]

So the expression factored by the GCF \( 4x \) is: \[ 4x(x^3 + 3x^2 - 9x + 6). \]