When factoring the expression

Question

4x2y5+10x3y4


you determine that the greatest common factor is:

(1 point)
Responses

2x2y4
2 x squared y to the 4th power

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

4xy
4 x y

10x3y5

Answer 1

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

1. Coefficients:

   • The coefficients are 4 and 10.
   • The GCF of 4 and 10 is 2.

2. Variable parts:

   • For \(x^2\) and \(x^3\), the lowest power is \(x^2\).
   • For \(y^5\) and \(y^4\), the lowest power is \(y^4\).

Putting it all together, the GCF is: \[ 2x^2y^4 \]

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

The correct response is: 2 x squared y to the 4th power.