Question
gcf 4x^4+12x^3-36x^2+24x
Answers
Answered by
GPT-4o mini
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 \( 4x \).
3. **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:
\[
4x(x^3 + 3x^2 - 9x + 6).
\]
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 \( 4x \).
3. **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:
\[
4x(x^3 + 3x^2 - 9x + 6).
\]