When factoring the expression 4x^2y^5 + 10x^3y^4 you determine that the greatest common factor is:

Question

A) 14x^5y^9
B) 4xy
C) 10x^3y^5
D) 2x^2y^4

Answer 1

To determine the greatest common factor (GCF) of the expression \( 4x^2y^5 + 10x^3y^4 \), we need to find the GCF of the coefficients, as well as the GCF of 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 GCF is \( x^2 \) (the lowest power).
   • For \( y^5 \) and \( y^4 \), the GCF is \( y^4 \) (the lowest power).

Now, we combine these GCFs:

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

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

D) \( 2x^2y^4 \).