Determine the greatest common factor of 24x3y4−15xy2−36x2y3%0D%0A24%0D%0A%0D%0A3%0D%0A%0D%0A4%0D%0A−%0D%0A15%0D%0A%0D%0A%0D%0A2%0D%0A−%0D%0A36%0D%0A%0D%0A2%0D%0A%0D%0A3%0D%0A:(1 point)%0D%0AResponses%0D%0A%0D%0A4xy2%0D%0A4%0D%0A%0D%0A%0D%0A2%0D%0A4 x y squared%0D%0A%0D%0Axy%0D%0A%0D%0A%0D%0Ax y%0D%0A%0D%0A3xy2%0D%0A3%0D%0A%0D%0A%0D%0A2%0D%0A3 x y squared%0D%0A%0D%0A3x2y2
To find the greatest common factor (GCF) of the given expression 24x^3y^4 - 15xy^2 - 36x^2y^3, we need to identify the highest power of each variable that appears in all terms.
Breaking down each coefficient and variable to its prime factors, we have:
24 = 2^3 * 3
15 = 3 * 5
36 = 2^2 * 3^2
x^3, x, and x^2 all have a common factor of x^1.
y^4, y^2, and y^3 all have a common factor of y^2.
Therefore, the GCF is 2^1 * 3^1 * x^1 * y^2, which simplifies to 6xy^2.