Find all rational zeros and factor f(x).
-$$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192$$
A) $- 4 , - 8,6 ; f ( x ) = ( x + 4 ) ( x + 8 ) ( x - 6 )$
B) $5,8 , - 12 ; f ( x ) = ( x - 5 ) ( x - 8 ) ( x + 12 )$
C) $4,8 , - 6 ; f ( x ) = ( x - 4 ) ( x - 8 ) ( x + 6 )$
D) $- 5 , - 8,12 ; f ( x ) = ( x + 5 ) ( x + 8 ) ( x - 12 )$

Question

Quizplus · Accepted Answer

To find the rational zeros, we use the Rational Root Theorem. The possible rational roots are factors of the constant term (-192) divided by factors of the leading coefficient (1). Testing the factors, we find that -4, -8, and 6 are zeros of $f(x)$. Substituting these values into $f(x)$ confirms they are zeros. Therefore, $f(x) = (x + 4)(x + 8)(x - 6)$.

Find All Rational Zeros and Factor F(x) f(x)=x3+6x2−40x−192f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192f(x)=x3+6x2−40x−192

Find All Rational Zeros and Factor F(x) $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192$