Review question

# What if the remainder when we divide by $x-k$ is $k$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8701

## Suggestion

1. Given that $f(x)=x^3+kx^2-2x+1$ and that when $f(x)$ is divided by $(x-k)$ the remainder is $k$, find the possible values of $k$.

What does the remainder theorem tell us?

1. When the polynomial $p(x)$ is divided by $(x-1)$ the remainder is $5$ and when $p(x)$ is divided by $(x-2)$ the remainder is $7$. Given that $p(x)$ may be written in the form $(x-1)(x-2)q(x)+Ax+B,$ where $q(x)$ is a polynomial and $A$ and $B$ are numbers, find the remainder when $p(x)$ is divided by $(x-1)(x-2)$.

Do we need to calculate $q(x)$?

How might we use the remainder theorem?