<s>[INST] Pre Calculus Synthetic Division two of the roots of the equation $2x^3-3x^2+px+q=0$ are $3$ and $-2$. Find the third root of the equation.
 [/INST] Hint:
Let $f(x) = 2x^{3} - 3x^{2} + px + q$. 
Since there are $3$ roots to a cubic equation, and $3$ and $-2$ are roots of $f(x)$, we can factor $f(x)$ as
$f(x) = (2x - k)(x-3)(x+2)$ 
where $k/2$ is the third root of $f(x)$. 
Since $f(x) = 2x^{3} - 3x^{2} + px + q$, we can expand the previous factorization of $f(x)$ to get linear equations which will allow us be able to solve for $k$. 
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