Solve the problem.
-Factor $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60$ given that $- 3$ is a zero.
A) $( x - 3 ) \left( 3 x ^ { 2 } + 7 x - 32 \right)$
B) $( x + 3 ) \left( 3 x ^ { 2 } + 7 x - 32 \right)$
C) $( x + 3 ) ( 3 x + 4 ) ( x - 5 )$
D) $( x - 3 ) ( 3 x - 4 ) ( x - 5 )$

Question

Quizplus · Accepted Answer

Given that $-3$ is a zero of the polynomial $f(x) = 3x^3 - 2x^2 - 53x - 60$, we can use synthetic division or polynomial division to divide the polynomial by $x + 3$. Doing so will yield a quotient of $3x^2 + 7x - 20$, which can be further factored into $(3x + 4)(x - 5)$. Therefore, the complete factorization of $f(x)$ is $(x + 3)(3x + 4)(x - 5)$, making option C correct.

Solve the Problem f(x)=3x3−2x2−53x−60f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60f(x)=3x3−2x2−53x−60

Solve the Problem $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60$