Remainder Theorem

Let us find remainder when p(x) is divided by g(x)

p(x) = x ³ − 3x ²   + 4x + 10

g(x) = x + 1

By Long Division

So, Remainder = 2

There is another method to find remainder by Remainder Theorem

Remainder Theorem

In remainder theorem

1. We put g(x) = 0, and find x.
2. Let x = a
3. Put a in p(x)
4. Remainder = p(a)

So, in our example

If  p(x) = x ³ − 3x ²   + 4x + 10 is divided by g(x) = x + 1

Putting g(x) = 0

        x + 1 = 0

           x =  − 1

  So, Remainder = p(−1)

    = (−1) ³   − 3(−1) ² + 4(−1) + 10

    = (−1)  − 3 × 1  − 4 + 10

    = −1 − 3 − 4 + 10

    = 2

So, Remainder = 2