Question 35

Explanation

Understand the concept of the remainder theorem below

Substitute $x = a$ into $f(x)$ with the result being the remainder.

Determining the value of $b$ in $g(x)$

$g(x) : (x - 1) \Rightarrow \text{remainder} = g(1)$. Because it is perfectly divisible, the remainder is equal to zero

So the function becomes $g(x) = x^3 + x^2 - x - 1$.

Determine the remainder of $g(x)$ divided by $x^2 - 1$ using long division

So the remainder of the division is $0$.