Determine the greatest common factor of 24x3y4−15xy2−36x2y3

Question

24
𝑥
3
𝑦
4
−
15
𝑥
𝑦
2
−
36
𝑥
2
𝑦
3
:(1 point)
Responses

3x2y2
3
𝑥
2
𝑦
2
3 x squared y squared

4xy2
4
𝑥
𝑦
2
4 x y squared

3xy2
3
𝑥
𝑦
2
3 x y squared

xy

Answer 1

To find the greatest common factor (GCF) of the expression \( 24x^3y^4 - 15xy^2 - 36x^2y^3 \), we need to identify the GCF for the coefficients (numerical parts) and the variables separately.

Step 1: Find the GCF of the coefficients.

The coefficients are: 24, -15, and -36.

• 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 \( 3 \).

Step 2: Find the GCF of the variable parts.

For \( x \):

• The terms have \( x^3, x^1, x^2 \).
• The smallest exponent is \( x^1 \).

For \( y \):

• The terms have \( y^4, y^2, y^3 \).
• The smallest exponent is \( y^2 \).

Combining these results, the GCF for the variable parts is \( xy^2 \).

Step 3: Combine the GCF of the coefficients and variables.

Thus, the GCF of the entire expression is: \[ 3xy^2 \]

The correct response is therefore:

3xy²