Question
Factor out the greatest common factor: -32x^3 - 4x^4yz^2
Answers
GPT-4o mini
To factor out the greatest common factor (GCF) from the expression \(-32x^3 - 4x^4yz^2\), we need to identify the GCF of the coefficients and the variable parts.
1. **Coefficients**: The coefficients of the terms are \(-32\) and \(-4\). The GCF of \(-32\) and \(-4\) is \(-4\).
2. **Variable Parts**:
- The first term has \(x^3\) and the second term has \(x^4\). The GCF for \(x^3\) and \(x^4\) is \(x^3\).
- The second term also has \(y\) and \(z^2\), but since these letters are only in the second term, they won’t contribute to the GCF.
Combining these, the overall GCF is:
\[
-4x^3
\]
Now we factor out \(-4x^3\) from the original expression:
\[
-32x^3 - 4x^4yz^2 = -4x^3(8 + x \cdot yz^2)
\]
Thus, the factored expression is:
\[
-4x^3(8 + xyz^2)
\]
1. **Coefficients**: The coefficients of the terms are \(-32\) and \(-4\). The GCF of \(-32\) and \(-4\) is \(-4\).
2. **Variable Parts**:
- The first term has \(x^3\) and the second term has \(x^4\). The GCF for \(x^3\) and \(x^4\) is \(x^3\).
- The second term also has \(y\) and \(z^2\), but since these letters are only in the second term, they won’t contribute to the GCF.
Combining these, the overall GCF is:
\[
-4x^3
\]
Now we factor out \(-4x^3\) from the original expression:
\[
-32x^3 - 4x^4yz^2 = -4x^3(8 + x \cdot yz^2)
\]
Thus, the factored expression is:
\[
-4x^3(8 + xyz^2)
\]