Question

When factoring the expression

4x2y5+10x3y4


you determine that the greatest common factor is:

(1 point)
Responses

14x5y9
14 x to the 5th power y to the 9th power

10x3y5
10 x cubed y to the 5th power

4xy
4 x y

2x2y4

Answer 1

To find the greatest common factor (GCF) of the expression \( 4x^2y^5 + 10x^3y^4 \), we need to determine the GCF of the coefficients and the GCF of the variables.

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

2. **For \(x\)**: The terms contain \(x^2\) and \(x^3\). The GCF of \(x^2\) and \(x^3\) is \(x^2\).

3. **For \(y\)**: The terms contain \(y^5\) and \(y^4\). The GCF of \(y^5\) and \(y^4\) is \(y^4\).

Now, we combine these factors to find the GCF:

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

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

Thus, the correct response from the options given is:

**2x^2y^4**.