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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

- We put g(x) = 0, and find x.
- Let x = a
- Put a in p(x)
- 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
**