Question

What is the remainder, the answer should be a integer using the remainder theorem.

Answer 1

The remainder theorem states that when P(x) is divided by x-a, then the remainder is P(a).

From the graph of P(x) given, if we divide it by x-3,

`\begin{gathered} (P(x))/(x-3),\text{ then the remainder will be P(3)} \\ \\ \text{Hence, the remainder is P(3)} \end{gathered}`

To get the remainder, we look at the graph.

The remainder P(3) from the graph means the value of y, when x = 3

By inspection, the value of y when x = 3 from the graph is 1.

This is as shown in the graph below;

Hence, the remainder which is P(3) is the point marked red on the graph.

This corresponds to y = 1

Therefore, the remainder is;

`P(3)=1`