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A polynomial $P(x)$ of degree $n \geq 2$ has a remainder of $9$ when it is divided by $(x+2)$ and a remainder of $-1$ when it is divided by $(x-3)$. Find the remainder of $P(x)$ when it is divided by $(x^2 -x-6)$.
We must have
$$p(x)=(x^2-x-6)q(x)+a(x+2)+9=(x^2-x-6)q(x)+a(x-3)-1$$ solving for $a$ we get $a=-2$ so the remainder is
Required, but never shown