Remainder Theorem
The Remainder theorem formula is used to find the remainder when a polynomial is divided by a linear polynomial.
Remainder Theorem
The Remainder theorem states that "when a polynomial is divided by a linear polynomial , then the remainder is "
Example
Find the remainder when the polynomial is divided by .
1 |
Here, quotient =
Remainder =
Verification :
Given, the divisor is , i.e. it is a factor of the given polynomial
Let
Substituting in ,
p(-1) = 3(-1)3 + (-1)2 + 2(-1) + 5
= 3(-1) + 1 – 2 + 5
= -3 + 4
= 1
Remainder = Value of p(x) at x = -1.
Hence proved the remainder theorem.
Alternatively,