Page 2 - Lesson Note-3 Reamainder and Factor Theorem Ch-2 POLYNOMIAL

a = 1

4
p (1) = (1) + (1) – 2(1) + (1) + 1
2
3
= 1 + 1 – 2 + 1 + 1
= 2

So, by using the remainder theorem, we can easily find the remainder after the division
of polynomial

3. Factor Theorem:
if p(x) is a polynomial of degree n≥1 and ‘a’ is any real number, then
I. (x− ) is a factor of p(x), if p(a) = 0, and

II. P (a) = 0 if (x – a) is a factor of p(x).

Example: 1
3
Check whether g(x) = x – 3 is the factor of p(x) = x - 4x + x + 6 using factor theorem.
2
Solution:
According to the factor theorem if x - 3 is the factor of p(x) then p (3) = 0, as the root
of x – 3 is 3.

Solution:
As x -1 is the factor so p(1) = 0

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