If I have a polynomial $f(x)$ and is divided by $(x- 3)$ and $(x + 6)$ the respective remainders are $7$ and $22$, what is the remainder when $f(x)$ is divided by $(x-3)(x + 6)$?
I tried it by doing:
$$f(x) =(x-3)(x+6)q(x) + ax+b $$ And, $a$ and $b$ comes out to be $-\dfrac53$ and $12$ respectively.
But I'm not sure how to solve any further. And kindly explain exactly how it's done