Using the remainder theorem
Find the remainder after division by
Supporting method: evaluating a polynomial at the divisor’s zero is a shortcut derived from polynomial division. The factor theorem and algebraic division are the required skills.
- The remainder when
is divided by is . - For division by
, evaluate . - A zero remainder also confirms a factor. This substitution rule here is for a linear divisor.
Example 1
No division needed
Find the remainder on division by
Example 2
Find the remainder on division by
Your turn
Question 1
Find the remainder when
Check answer
Question 2
Find the remainder when
Check answer
Question 3
Find the remainder when
Check answer
Question 4
Find the remainder when
Check answer
Question 5
Find the remainder when
Check answer
Find the remainder when
Find the remainder when
Find the remainder when
Find the remainder when
Find the remainder when