Factor the trinomial x 2 n − 5 x n − 36 x ^ { 2 n } - 5 x ^ { n } - 36 x 2 n − 5 x n − 36 . (Assume that n represents a positive integer.)A) ( x n − 9 ) ( x n − 4 ) \left( x ^ { n } - 9 \right) \left( x ^ { n } - 4 \right) ( x n − 9 ) ( x n − 4 ) B) ( x 2 n − 9 ) ( x 2 n + 4 ) \left( x ^ { 2 n } - 9 \right) \left( x ^ { 2 n } + 4 \right) ( x 2 n − 9 ) ( x 2 n + 4 ) C) ( x n − 9 ) ( x n + 4 ) \left( x ^ { n } - 9 \right) \left( x ^ { n } + 4 \right) ( x n − 9 ) ( x n + 4 ) D) ( x 2 n + 9 ) ( x 2 n − 4 ) \left( x ^ { 2 n } + 9 \right) \left( x ^ { 2 n } - 4 \right) ( x 2 n + 9 ) ( x 2 n − 4 ) E) ( x n + 9 ) ( x n − 4 ) \left( x ^ { n } + 9 \right) \left( x ^ { n } - 4 \right) ( x n + 9 ) ( x n − 4 )

Question

Factor the trinomial   x 2 n − 5 x n − 36 x ^ { 2 n } - 5 x ^ { n } - 36 x 2 n − 5 x n − 36   . (Assume that n represents a positive integer.)A)    ( x n − 9 )  ( x n − 4 )  \left( x ^ { n } - 9 \right)  \left( x ^ { n } - 4 \right)  ( x n − 9 )  ( x n − 4 )  B)    ( x 2 n − 9 )  ( x 2 n + 4 )  \left( x ^ { 2 n } - 9 \right)  \left( x ^ { 2 n } + 4 \right)  ( x 2 n − 9 )  ( x 2 n + 4 )  C)    ( x n − 9 )  ( x n + 4 )  \left( x ^ { n } - 9 \right)  \left( x ^ { n } + 4 \right)  ( x n − 9 )  ( x n + 4 )  D)    ( x 2 n + 9 )  ( x 2 n − 4 )  \left( x ^ { 2 n } + 9 \right)  \left( x ^ { 2 n } - 4 \right)  ( x 2 n + 9 )  ( x 2 n − 4 )  E)    ( x n + 9 )  ( x n − 4 )  \left( x ^ { n } + 9 \right)  \left( x ^ { n } - 4 \right)  ( x n + 9 )  ( x n − 4 )

Patrina Gayle · Accepted Answer

Final Answer : C, Explanation :   The trinomial can be factored by looking for two numbers that multiply to -36 and add to -5. Those numbers are -9 and +4. Therefore, the factored form is   ( x n − 9 ) ( x n + 4 ) (x^n - 9)(x^n + 4) ( x n − 9 ) ( x n + 4 )  .

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