2018 BIMC keystage3-IWYMIC individual Question 7

Let $P(x)=x^4+ax^3+bx^2+cx+d$, where $a,b,c$ and $d$ are real constants. Suppose $P(1)=7$, $P(2)=52$ and $P(3)=97$. Find the value of $\dfrac{P(9)+P(-5)}4$.

Answer: ______