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**tttcomrader** By the Remainder's Theorem, in which we learned in Algebra, we know that the possible zeroes for a polynoimal is: $\displaystyle \frac { factors \ of \ constant \ term }{ factors \ of \ leading \ coefficient } $.

Therefore, the possible list of zeroes here is: $\displaystyle \{ - \frac {1}{4} , - \frac {1}{2} , - 1 , 1, \frac {1}{2}, \frac {1}{4} \} $

Then just try and find which one would be your zero. I plugged in $\displaystyle \frac {1}{2} $ and it gave me zero, so that is one of your critical points.