\(P\left(1\right)=4-5+1-2=-2\)
\(P\left(-1\right)=-4-5-1-2=-12\)
\(P\left(-2\right)=4\cdot\left(-8\right)-5\cdot4-2-2=-56\)
\(P\left(-\dfrac{3}{2}\right)=4\cdot\dfrac{-27}{8}-5\cdot\dfrac{9}{4}+\dfrac{-3}{2}-2\)
\(=\dfrac{-27}{2}-\dfrac{45}{4}+\dfrac{-3}{2}-2=-\dfrac{113}{4}\)