A polynomial $P(x)=x^4+3x^3-5x^2+7x+9$ is divided separately by $(x-2)$ and $(x+1)$, giving remainders $R_1$ and $R_2$, respectively. Find the value of $\dfrac{R_1+R_2}{2}$.
Solution
✅ Correct Option: 1
By the Remainder Theorem, $R_1=P(2)$ and $R_2=P(-1)$. $P(2)=16+24-20+14+9=43$ $P(-1)=1-3-5-7+9=-5$ $\dfrac{R_1+R_2}{2}=\dfrac{43-5}{2}=19$.