Question

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

2x
2 x

4
4

6x
6 x

4x

Answer 1

To find the Greatest Common Factor (GCF) of the polynomial \(4x^4 + 12x^3 - 36x^2 + 24x\), we will first factor out any common factors from each term.

1. Break down each term:
- \(4x^4\): has a factor of \(4\) and \(x^4\)
- \(12x^3\): has a factor of \(12\) and \(x^3\)
- \(-36x^2\): has a factor of \(-36\) and \(x^2\)
- \(24x\): has a factor of \(24\) and \(x\)

2. Identify the GCF of the coefficients:
- The coefficients are \(4\), \(12\), \(-36\), and \(24\).
- The GCF of \(4\), \(12\), \(36\), and \(24\) is \(12\).

3. Identify the GCF of the variable parts:
- The variable parts are \(x^4\), \(x^3\), \(x^2\), and \(x\).
- The GCF of \(x^4\), \(x^3\), \(x^2\), and \(x\) is \(x\).

4. Now, combine the GCF of the coefficients and the variables, which gives:
\[
GCF = 4x
\]

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