Introduction
This is a topic of chapter polynomial and in the name factor is coming which means that we are going to deal with factor of polynomials.
Concept of Factor theorem
You have studied about checking formula of division which is divided=divisor×quotient+remainder it shows us that our division is correct or not. We have studied in previous classes . Same thing we will do but with the polynomial during divide if the divisor is a factor of dividend then the remainder will zero the same concept wil apply in the factor theorem .
Application of factor theorem
Let p(x) is a polynomial with a degree n which is greater than 1 and let a be a real number .
If p(x) is dividend by x-a then p(a)=0 , the remainder is 0 that shows that x-a is factor of polynomial p(x).
Note:if the remainder come 0 then it's show that the given expression is a factor of given polynomial.
Example :
Using factor theorem show that ( x-2) is a factor of (x³-8)
Solution:
Let p(x)=(x³-8)
X-2=0
X=2
By factor theorem, p(x) is divided by (x-2) if p(2)=0
P(2)=0
(2)²-8=0
8-8=0
0=0
Hence, remainder is 0
Therefore, (x-2) is a factor of x³-8.
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