Review question

# What is the remainder when $p_n (x)$ is divided by $p_{n-1} (x)$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5276

## Suggestion

Let $n \ge 2$ be an integer and $p_n (x)$ be the polynomial $p_n (x) = (x-1) + (x-2) + \cdots + (x-n).$ What is the remainder when $p_n (x)$ is divided by $p_{n-1} (x)$?

1. $\dfrac{n}{2}$;

2. $\dfrac{n+1}{2}$;

3. $\dfrac{n^2+n}{2}$;

4. $\dfrac{-n}{2}$.

The terms in $p_n (x)$ follow a sequence - can we sum this?

What value of $x$ makes $p_{n-1}(x)$ zero?