Factor f(x) into linear factors given that k is a zero of f(x).
-$\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } - 75 \mathrm { x } - 250 ; \mathrm { k } = - 5$ (multiplicity 2 $)$
A) $f ( x ) = ( x + 5 ) ^ { 2 } ( x + 10 )$
B) $f ( x ) = ( x + 5 ) ^ { 2 } ( x - 10 )$
C) $f ( x ) = ( x + 10 ) ( x + 5 ) ( x - 5 )$
D) $f ( x ) = ( x - 5 ) ^ { 2 } ( x - 10 )$

Question

Quizplus · Accepted Answer

Given that $k = -5$ is a zero of $f(x)$ with multiplicity 2, it means $(x + 5)^2$ is a factor of $f(x)$. To find the third factor, we can divide $f(x)$ by $(x + 5)^2$ or use synthetic division. The remaining linear factor must result in the original polynomial when multiplied by $(x + 5)^2$, leading to $f(x) = (x + 5)^2(x - 10)$, which matches option B.

Factor F(x) into Linear Factors Given That K Is a Zero