Find a Factored Form with Integer Coefficients of the Polynomial $$f ( x ) = 10 x ^ { 5 } - 41 x ^ { 4 } + 52 x ^ { 3 } - 17 x ^ { 2 } - 8 x + 4$$

Multiple Choice

Find a factored form with integer coefficients of the polynomial f shown in the figure. $$f ( x ) = 10 x ^ { 5 } - 41 x ^ { 4 } + 52 x ^ { 3 } - 17 x ^ { 2 } - 8 x + 4$$

A) $( 2 x + 5 ) \left( x ^ { 2 } - 2 \right) ( x - 1 ) ( x - 2 )$
B) $( 2 x + 5 ) ( 2 x - 1 ) ( x - 1 ) ^ { 2 } ( x - 2 )$
C) $( 5 x - 2 ) ( 2 x - 1 ) ( x - 1 ) ^ { 2 } ( x + 2 )$
D) $( 5 x + 2 ) ( 2 x - 1 ) ( x - 1 ) ^ { 2 } ( x - 2 )$
E) $x ( 5 x + 2 ) ( 2 x - 1 ) ( x - 1 ) ( x - 2 )$