Question

When factoring the expression

4x^2 y^5 + 10x^3 y^4


you determine that the greatest common factor is:

(1 point)

Answer 1

To find the greatest common factor (GCF) of the expression \(4x^2 y^5 + 10x^3 y^4\), we will look at the coefficients and the variables separately.

1. **Coefficients**:
- The coefficients are 4 and 10.
- The GCF of 4 and 10 is 2.

2. **Variables**:
- For \(x^2\) and \(x^3\), the GCF is \(x^2\) (the lowest power of \(x\)).
- For \(y^5\) and \(y^4\), the GCF is \(y^4\) (the lowest power of \(y\)).

Now, we combine the GCFs of the coefficients and the variables:

\[
\text{GCF} = 2x^2y^4
\]

Thus, the greatest common factor of the expression \(4x^2 y^5 + 10x^3 y^4\) is:

\[
\boxed{2x^2y^4}
\]