A Polynomial F ( X ) with Real Coefficients and Leading

Multiple Choice

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R. $4 + 1 i , - 9 + i \text {; degree } 4$

A) $\left( x ^ { 2 } - 8 x + 17 \right) \left( x ^ { 2 } + 18 x + 82 \right)$
B) $\left( x ^ { 2 } - 8 x + 16 \right) \left( x ^ { 2 } + 18 x + 81 \right)$
C) $\left( x ^ { 2 } - 8 x + 81 \right) \left( x ^ { 2 } + 18 x + 17 \right)$
D) $\left( x ^ { 2 } - 8 x + 17 \right) \left( x ^ { 2 } + 18 x + 16 \right)$
E) $\left( x ^ { 2 } - 8 x + 16 \right) \left( x ^ { 2 } + 18 x + 82 \right)$