If $x(x(x+1)+2)+3=x^{3}+x^{2}+x-6$ then $x$ is equal to
(A) 11
(B) -9
(C) -4 or 3
(D) -1 or 0
(E) -2

## Part B: Each correct answer is worth 6.
If $x(x(x+1)+2)+3=x^{3}+x^{2}+x-6$ then $x$ is equal to
(A) 11
(B) -9
(C) -4 or 3
(D) -1 or 0
(E) -2

## Solution

$$
\begin{aligned}
x(x(x+1)+2)+3 & =x\left(x^{2}+x+2\right)+3 \\
& =x^{3}+x^{2}+2 x+3
\end{aligned}
$$

Since $x^{3}+x^{2}+2 x+3=x^{3}+x^{2}+x-6$

$$
\begin{aligned}
2 x+3 & =x-6 \\
x & =-9
\end{aligned}
$$

ANSWER: (B)

## Part B: