Write a linear factorization of the function.
-$$f ( x ) = x ^ { 4 } - 18 x ^ { 3 } + 82 x ^ { 2 } - 18 x + 81$$
A) $f ( x ) = ( x - 9 ) ^ { 2 } ( x + i ) ( x - i )$
B) $f ( x ) = ( x - 9 ) ( x - 8 ) ( x + i ) ( x - i )$
C) $f ( x ) = ( x - 9 ) ( x - 7 ) ( x + i ) ( x - i )$
D) $f ( x ) = ( x - 9 ) ( x + i ) ( x - i )$

Question

Quizplus · Accepted Answer

The given polynomial can be factored as $f(x) = (x - 9)^2(x^2 + 1)$, where $x^2 + 1$ can be further factored into $(x + i)(x - i)$, resulting in the linear factorization $f(x) = (x - 9)^2(x + i)(x - i)$.

Write a Linear Factorization of the Function f(x)=x4−18x3+82x2−18x+81f ( x ) = x ^ { 4 } - 18 x ^ { 3 } + 82 x ^ { 2 } - 18 x + 81f(x)=x4−18x3+82x2−18x+81

Write a Linear Factorization of the Function $f ( x ) = x ^ { 4 } - 18 x ^ { 3 } + 82 x ^ { 2 } - 18 x + 81$