I have been presented with the following question, I have no idea where to start with the methodology of it. in the question it does not state what branch of mathematics this is so I do not know what to read to study it.
The question is as follows:
When a polynomial of degree two or more is divided by a linear function of the form $(x-a)$, then we get:
$$\frac{P(x)}{x-a} = Q(x)+\frac{r}{x-a}$$
Where $Q(x)$ is a polynomial of degree one less than $P(x)$ and $r$ is a constant.
Find the values of $r_1$ and $r_2$ when the following cubic is divided by $(x-7)$ and $(x+9)$ respectively.
$$P(x) = -8x^4+16x^3-6x^2-4x+2$$
If someone could please show me the methodology to complete this question and find $r_1$ and $r_2$ I would be extremely grateful, thank you.
Hint: rewrite as $P(x)=(x-a)Q(x) + r$, then substitute $x=a$ to get $r=P(a)$.
For the approach in the general case, lookup the Euclidian division of polynomials.