Using the Factors $( - 5 x + 2 )$ And $( x - 1 )$

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$ , find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

A) $f ( x ) = ( - 5 x + 2 ) ( - 5 x + 2 ) ( 2 x - 1 ) ( x - 1 )$
B) $f ( x ) = ( - 5 x + 2 ) ( - x - 5 ) ( 2 x - 1 ) ( x - 1 )$
C) $f ( x ) = ( - 5 x + 2 ) ^ { 2 } ( 2 x - 1 ) ( x + 1 )$
D) $f ( x ) = ( - 5 x + 2 ) ( - x + 5 ) ^ { 2 } ( x + 1 )$
E) $f ( x ) = ( - 5 x + 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$

Correct Answer:

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