Determine the greatest common factor of 24x3y4−15xy2−36x2y3 :(1 point) Responses 3x2y2 3 x squared y squared 4xy2 4 x y squared 3xy2 3 x y squared xy x y

Answer 1

To determine the greatest common factor (GCF) of the expression \( 24x^3y^4 - 15xy^2 - 36x^2y^3 \), we can start by finding the GCF of the coefficients (24, -15, and -36) and the variables.

1. Find the GCF of the coefficients:

   • The factors of 24 are \( 1, 2, 3, 4, 6, 8, 12, 24 \).
   • The factors of 15 are \( 1, 3, 5, 15 \).
   • The factors of 36 are \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \).
   • The common factors are \( 1, 3 \), so the GCF of the coefficients is \( 3 \).

2. Find the GCF of the variable parts:

   • For \( x \): in \( 24x^3y^4 \), we have \( x^3 \); in \( -15xy^2 \), we have \( x^1 \); in \( -36x^2y^3 \), we have \( x^2 \). The GCF of \( x^3, x^1, x^2 \) is \( x^1 = x \).
   • For \( y \): in \( 24x^3y^4 \), we have \( y^4 \); in \( -15xy^2 \), we have \( y^2 \); in \( -36x^2y^3 \), we have \( y^3 \). The GCF of \( y^4, y^2, y^3 \) is \( y^2 \).

3. Combine the GCF components:

   • Therefore, the GCF of the entire expression is \( 3xy^2 \).

Putting it all together, the greatest common factor of \( 24x^3y^4 - 15xy^2 - 36x^2y^3 \) is \( \boxed{3xy^2} \).