Factor 26r3s + 52r5 + 39r2s4: What is the Resulting Expression?

To factor the expression 26r³s + 52r⁵ + 39r²s⁴, we first look for the greatest common factor (GCF) of the coefficients and the variables in each term.

The coefficients are 26, 52, and 39. The GCF of these numbers is 13. Now let’s identify the variables:

• The first term has r³s.
• The second term has r⁵.
• The third term has r²s⁴.

For the variable r, the lowest degree is r². For the variable s, the lowest degree is s (since the first term has s and the others have higher powers of s).

Now we can factor out the GCF, which is 13r²s, from each term:

• From 26r³s: 13r²s × 2r
• From 52r⁵: 13r²s × 4r³
• From 39r²s⁴: 13r²s × 3s³

Putting it all together, we have:

13r²s(2r + 4r³ + 3s³)

This is the factored form of the original expression. Thus, the resulting expression after factoring is:

13r²s(2r + 4r³ + 3s³).