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Question

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

4x
4 x

4
4

2x
2 x

6x

Answer 1

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

1. Identify the coefficients:

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

2. Identify the variable part:

   • The terms have \(x^4\), \(x^3\), \(x^2\), and \(x\). The lowest power of \(x\) among these terms is \(x\).

3. Combine the GCF of the coefficients with the GCF of the variable parts:

   • Thus, the GCF of the entire polynomial is \(4x\).

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