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

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

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

Answer

Explanation:

Step1: Find the GCF of coefficients

The coefficients are (26), (52), and (39). The GCF of (26 = 2\times13), (52=4\times13), (39 = 3\times13) is (13).

Step2: Find the GCF of variables

For the (r) - terms: (r^{3}), (r^{5}), (r^{2}). The lowest power of (r) is (r^{2}). For the (s) - terms: (s), no (s) in the second term ((s^{0})), (s^{4}). The lowest power of (s) is (s^{0}) (but since we want a common factor that can be factored out from all terms, and considering the first term has (s) and the second term has no (s) in a non - trivial way for factoring across all three terms, we note that the GCF of the variable part considering all three terms for (r) is (r^{2}) (because (r^{2}) divides (r^{3}), (r^{5}), and (r^{2})).

Step3: Factor out the GCF

[ \begin{align*} 26r^{3}s + 52r^{5}-39r^{2}s^{4}&=13r^{2}(2rs + 4r^{3}-3s^{4}) \end{align*} ]

Answer:

(13r^{2}(2rs + 4r^{3}-3s^{4})) (corresponds to the third option (13r^{2}(2rs + 4r^{3}-3s^{4})))