Write a linear factorization of the function.
-$$f ( x ) = x ^ { 4 } + 61 x ^ { 2 } + 900$$
A) $f ( x ) = ( x + 30 i ) ^ { 4 }$
B) $f ( x ) = ( x + i ) ( x - i ) ( x + 30 i ) ( x - 30 i )$
C) $f ( x ) = \left( x ^ { 2 } + 30 i \right) \left( x ^ { 2 } - 30 i \right)$
D) $f ( x ) = ( x + 5 i ) ( x - 5 i ) ( x + 6 i ) ( x - 6 i )$

Question

Quizplus · Accepted Answer

The polynomial can be factored into quadratic factors with complex roots: $x^2 + 25$ and $x^2 + 36$, which further factor into linear factors with imaginary roots: $(x + 5i)(x - 5i)(x + 6i)(x - 6i)$.

Write a Linear Factorization of the Function f(x)=x4+61x2+900f ( x ) = x ^ { 4 } + 61 x ^ { 2 } + 900f(x)=x4+61x2+900

Write a Linear Factorization of the Function $f ( x ) = x ^ { 4 } + 61 x ^ { 2 } + 900$