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

Question

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

Answer 1

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

1. Coefficients:

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

2. Variable \(x\):

   • The powers of \(x\) are \(x^2\) and \(x^3\).
   • The GCF is \(x^{\min(2, 3)} = x^2\).

3. Variable \(y\):

   • The powers of \(y\) are \(y^5\) and \(y^4\).
   • The GCF is \(y^{\min(5, 4)} = y^4\).

Putting it all together, the GCF of \(4x^2y^5\) and \(10x^3y^4\) is:

\[ 2x^2y^4 \]

Thus, the correct answer is:

C) \(2x^2y^4\)