$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$
A) $t ^ { 3 } - 4 t ^ { 2 } + 12 t - 144$
B) $t ^ { 3 } - 4 t ^ { 2 } + 84 t - 144$
C) $t ^ { 3 } - 16 t ^ { 2 } + 84 t - 144$
D) $t ^ { 3 } - 16 t ^ { 2 } + 12 t - 144$
E) none of the above

Question

$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$ 
A) $t ^ { 3 } - 4 t ^ { 2 } + 12 t - 144$
B) $t ^ { 3 } - 4 t ^ { 2 } + 84 t - 144$
C) $t ^ { 3 } - 16 t ^ { 2 } + 84 t - 144$
D) $t ^ { 3 } - 16 t ^ { 2 } + 12 t - 144$
E) none of the above

Quizplus · Accepted Answer

To evaluate $g(x) = x^2(x + 2)$ at $x = t - 6$, substitute $x = t - 6$ into the function:$$g(t - 6) = (t - 6)^2[(t - 6) + 2]$$$$= (t - 6)^2(t - 4)$$$$= (t^2 - 12t + 36)(t - 4)$$$$= t^3 - 4t^2 - 12t^2 + 48t + 36t - 144$$$$= t^3 - 16t^2 + 84t - 144$$This simplifies to the expression in choice C.

Evaluate (if possible) the function g(x)=x2(x+2) at x=t−6. Simplify the result. \text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. } Evaluate (if possible) the function g(x)=x2(x+2) at x=t−6. Simplify the result.

$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$