Question

factor $26r^{3}s + 52r^{5} - 39r^{2}s^{4}$. what is the resulting expression?
$13(2r^{3}s + 4r^{5} - 3r^{2}s^{4})$
$13r^{2}s(2r + 4r^{3} - 3s^{3})$
$13r^{2}(2rs + 4r^{3} - 3s^{4})$
$13r^{2}(26r^{3}s + 52r^{5} - 39r^{2}s^{4})$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 26, 52, 39. Their greatest common factor (GCF) is 13.

Step2: Find GCF of $r$-terms

For $r^3$, $r^5$, $r^2$, the GCF is $r^2$.

Step3: Find GCF of $s$-terms

For $s^1$, $s^0$, $s^4$, the GCF is $s^0=1$.

Step4: Factor out overall GCF

Factor $13r^2$ from each term:
$26r^3s = 13r^2 \cdot 2rs$
$52r^5 = 13r^2 \cdot 4r^3$
$-39r^2s^4 = 13r^2 \cdot (-3s^4)$
Combine: $13r^2(2rs + 4r^3 - 3s^4)$

Step5: Verify options

Match the factored expression to the choices.

Answer:

13$r^2$(2$rs$ + 4$r^3$ - 3$s^4$) (the third option)