What is the resulting expression when factoring 26r^3s, 52r^5, and 39r^2s^4?

To factor the expression involving the terms 26r³s, 52r⁵, and 39r²s⁴, we need to find the greatest common factor (GCF) for the coefficients and the variable parts separately.

Step 1: Factor the Coefficients

The coefficients are 26, 52, and 39.

• Factors of 26: 1, 2, 13, 26
• Factors of 52: 1, 2, 4, 13, 26, 52
• Factors of 39: 1, 3, 13, 39

The GCF of the coefficients (26, 52, and 39) is 13.

Step 2: Factor the Variable Parts

Now, let’s consider the variable parts:

• For r: The powers are 3 (from 26r³s), 5 (from 52r⁵), and 2 (from 39r²s⁴).
• The minimum power of r is r².
• For s: The presence is 1 (from 26r³s), 0 (from 52r⁵ since it has no ‘s’), and 4 (from 39r²s⁴).
• The minimum power of s is s⁰ = 1 (no ‘s’ in the second term).

Combining the Results

Now we can combine the GCF of the coefficients with the GCF of the variables:

The final factored form of the expression 26r³s + 52r⁵ + 39r²s⁴ is:

13r² (2rs + 4r³ + 3s³)

This expression reflects the common factors and is simplified, making it easier to handle in further calculations.