For the given f(x $$f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$$
-$$f ( x ) = - 3 x ^ { 3 } - 18 x ^ { 2 } - 20 x + 16 ; g ( x ) = x + 4$$
A) $3 x ^ { 2 } + 4 x - 4 ; x \neq 4$
B) $- 3 x ^ { 2 } - 6 x + 4 ; x \neq - 4$
C) $3 x ^ { 2 } - 4 x + 4 ; x \neq - 4$
D) $- 3 x ^ { 2 } - 6 x + 4 ; x \neq 4$

Question

Quizplus · Accepted Answer

To find $\frac{f(x)}{g(x)}$, we divide $f(x)$ by $g(x)$. Given $f(x) = -3x^3 - 18x^2 - 20x + 16$ and $g(x) = x + 4$, we perform polynomial long division or synthetic division. The division results in $-3x^2 - 6x + 4$. The domain of $\frac{f(x)}{g(x)}$ excludes values that make $g(x) = 0$, which occurs when $x = -4$. Therefore, the correct choice is $-3x^2 - 6x + 4$ with $x \neq -4$.

For the Given F(x - f(x)=−3x3−18x2−20x+16;g(x)=x+4f ( x ) = - 3 x ^ { 3 } - 18 x ^ { 2 } - 20 x + 16 ; g ( x ) = x + 4f(x)=−3x3−18x2−20x+16;g(x)=x+4

For the Given F(x - $f ( x ) = - 3 x ^ { 3 } - 18 x ^ { 2 } - 20 x + 16 ; g ( x ) = x + 4$