hich of the following is the GCF of the polynomial 3x^4+3x^3−9x^2+12x ?

Answer 1

To find the greatest common factor (GCF) of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\), we first identify the coefficients and the variable parts of each term:

1. The terms are:

   • \(3x^4\)
   • \(3x^3\)
   • \(-9x^2\)
   • \(12x\)

2. Finding the GCF of the coefficients:

   • The coefficients are 3, 3, -9, and 12.
   • The GCF of \(3, 3, -9, 12\) is 3.

3. Finding the GCF of the variable parts:

   • The variable parts are \(x^4\), \(x^3\), \(x^2\), and \(x\).
   • The GCF of \(x^4, x^3, x^2, x\) is \(x^1\) or simply \(x\).

4. Combining the GCFs:

   • The overall GCF of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\) is the product of the GCF of the coefficients and the GCF of the variable parts, which is: \[ \text{GCF} = 3x. \]

Therefore, the GCF of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\) is \(\boxed{3x}\).