Find all complex zeros of the polynomial function, and write the polynomial in completely factored form.
-$$f ( x ) = x ^ { 3 } - x ^ { 2 } + 25 x - 25$$
A) $f ( x ) = ( x - 1 ) ( x + 5 i ) ( x - 5 i )$
B) $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 25 )$
C) $f ( x ) = ( x - 1 ) ( x + 5 ) ( x - 5 )$
D) $f ( x ) = ( x - 25 ) ( x + i ) ( x - i )$

Question

Quizplus · Accepted Answer

The polynomial can be factored as $f(x) = (x - 1)(x^2 + 25)$, where $x^2 + 25 = 0$ gives the complex roots $x = \pm 5i$, leading to the completely factored form $f(x) = (x - 1)(x + 5i)(x - 5i)$.

Find All Complex Zeros of the Polynomial Function, and Write f(x)=x3−x2+25x−25f ( x ) = x ^ { 3 } - x ^ { 2 } + 25 x - 25f(x)=x3−x2+25x−25

Find All Complex Zeros of the Polynomial Function, and Write $f ( x ) = x ^ { 3 } - x ^ { 2 } + 25 x - 25$