Question

Using remainder theorem, find the remainder when:
x³ − ax² + 2x − a is divided by (x − a)

Answer 1

We have:
$x-a=0\Rightarrow x=a$
By the remainder theorem, we know that when f(x) is divided by (x $-$ a), the remainder is f(a).
Thus, we have:
$$\begin{gathered} f\left(x\right)=\left(x^3-a{x}^2+2x-a\right) \\ \therefore f\left(a\right)=\left(a^3-a\times a^2+2\times a-a\right) \\ =\left(a^3-a^3+2a-a\right) \\ =a \end{gathered}$$
​Hence, the required remainder is a.