Completely factor the polynomial x 3 − 57 x + 56 x ^ { 3 } - 57 x + 56 x 3 − 57 x + 56 given one of its factors is x-7 .A) ( x − 7 ) ( x − 1 ) ( x + 8 ) ( x - 7 ) ( x - 1 ) ( x + 8 ) ( x − 7 ) ( x − 1 ) ( x + 8 ) B) ( x − 7 ) ( x − 2 ) ( x + 16 ) ( x - 7 ) ( x - 2 ) ( x + 16 ) ( x − 7 ) ( x − 2 ) ( x + 16 ) C) ( x − 7 ) ( x + 2 ) ( x + 24 ) ( x - 7 ) ( x + 2 ) ( x + 24 ) ( x − 7 ) ( x + 2 ) ( x + 24 ) D) ( x − 7 ) ( x − 3 ) ( x + 32 ) ( x - 7 ) ( x - 3 ) ( x + 32 ) ( x − 7 ) ( x − 3 ) ( x + 32 ) E) ( x − 7 ) ( x + 1 ) ( x − 9 ) ( x - 7 ) ( x + 1 ) ( x - 9 ) ( x − 7 ) ( x + 1 ) ( x − 9 )

Question

Completely factor the polynomial   x 3 − 57 x + 56 x ^ { 3 } - 57 x + 56 x 3 − 57 x + 56   given one of its factors is x-7 .A)    ( x − 7 )  ( x − 1 )  ( x + 8 )  ( x - 7 )  ( x - 1 )  ( x + 8 )  ( x − 7 )  ( x − 1 )  ( x + 8 )  B)    ( x − 7 )  ( x − 2 )  ( x + 16 )  ( x - 7 )  ( x - 2 )  ( x + 16 )  ( x − 7 )  ( x − 2 )  ( x + 16 )  C)    ( x − 7 )  ( x + 2 )  ( x + 24 )  ( x - 7 )  ( x + 2 )  ( x + 24 )  ( x − 7 )  ( x + 2 )  ( x + 24 )  D)    ( x − 7 )  ( x − 3 )  ( x + 32 )  ( x - 7 )  ( x - 3 )  ( x + 32 )  ( x − 7 )  ( x − 3 )  ( x + 32 )  E)    ( x − 7 )  ( x + 1 )  ( x − 9 )  ( x - 7 )  ( x + 1 )  ( x - 9 )  ( x − 7 )  ( x + 1 )  ( x − 9 )

Irabelle Labomarel · Accepted Answer

Final Answer : A, Explanation :   Given that   x − 7 x - 7 x − 7   is a factor, we can perform polynomial division or use synthetic division to find the other factors. The correct complete factorization of   x 3 − 57 x + 56 x^3 - 57x + 56 x 3 − 57 x + 56   is   ( x − 7 ) ( x − 1 ) ( x + 8 ) (x - 7)(x - 1)(x + 8) ( x − 7 ) ( x − 1 ) ( x + 8 )  , which simplifies to the given polynomial when multiplied out.

Completely factor the polynomial $x ^ { 3 } - 57 x + 56$ given one of its factors is x-7 .

A) $(x - 7) (x - 1) (x + 8)$
B) $(x - 7) (x - 2) (x + 16)$
C) $(x - 7) (x + 2) (x + 24)$
D) $(x - 7) (x - 3) (x + 32)$
E) $(x - 7) (x + 1) (x - 9)$

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