Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form.
-$f ( x ) = 3 x ^ { 3 } - 8 x ^ { 2 } - 5 x + 6 ; c = - 1$ is a zero
A) $\frac { 3 } { 2 } , - 3 ; f ( x ) = ( 3 x - 2 ) ( x - 3 ) ( x + 1 )$
B) $- 3,1 , \frac { 3 } { 2 } ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x + 3 )$
C) $\frac { 2 } { 3 } , 3 ; f ( x ) = ( 3 x - 2 ) ( x - 3 ) ( x + 1 )$
D) $- 3 , \frac { 2 } { 3 } , 1 ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x + 3 )$

Question

Quizplus · Accepted Answer

Given that $c = -1$ is a zero, we can perform synthetic division or use the fact that $x + 1$ is a factor of $f(x)$. Factoring $f(x)$ by dividing it by $x + 1$ will give us a quadratic equation, which we can then solve or factor further to find the remaining zeros. The correct remaining zeros are $\frac{2}{3}$ and $3$, which means the factored form of $f(x)$ includes $(x + 1)$, $(3x - 2)$, and $(x - 3)$, making option C correct.

Find the Remaining Zeros of F(x)given That C Is a Zero