1. Remainder Theorem
What’s left over?

2. What is remainder? When dealing with numbers what does remainder mean?
Is the remainder always smaller than the number you are dividing by?
Why?

3. Using remainder
732 ÷ 13
We can use our answer to write a sum involving the remainder.
726 = 13 x

4. Algebra Remainder Activity: f(x) = x3 + 3x2 – 2x + 1
Divide f(x) by (x + 1). (you should get a remainder
Calculate f(-1)
What do you notice?
Now divide f(x) by (x – 2). Is the remainder the same as f(2) ?

5. The Remainder Theorem
What you have found is a connection very similar to the factor theorem :
If you divide a polynomial f(x) by (x – a), the remainder is equal to the value of f(a).

6. Example f(x) = 2x3 + ax2 + bx + 4
When divided by (x – 1) the remainder is 1.
When divided by (x + 1) the remainder is 3.
Find a and b.