If 2x^{2}-dx+(31-d^{2})x+5 has a factor of x - d, what is the value of d if d is an integer?
Let:
$\displaystyle f(x)=2x^2-dx+(31-d^2)x+5$
If $\displaystyle f(x)$ has a factor of $\displaystyle x-d$ then $\displaystyle f(d)=0$.
Hint: use the rational roots theorem on the resulting cubic in $\displaystyle d$.