Answer
$P\left( -\dfrac{1}{2} \right)=\dfrac{365}{32}$
Work Step by Step
Substituting $x$ with $
-\dfrac{1}{2}
$ in the given polynomial equation, $P(x)=3x^5-9x+7,$ then,
\begin{array}{l}\require{cancel}
P\left( -\dfrac{1}{2} \right)=3\left( -\dfrac{1}{2} \right)^5-9\left( -\dfrac{1}{2} \right)+7
\\\\
P\left( -\dfrac{1}{2} \right)=3\left( -\dfrac{1}{32} \right)-9\left( -\dfrac{1}{2} \right)+7
\\\\
P\left( -\dfrac{1}{2} \right)=-\dfrac{3}{32}+\dfrac{9}{2}+7
\\\\
P\left( -\dfrac{1}{2} \right)=\dfrac{365}{32}
.\end{array}
