It states that “ When a polynomial p(X) leaves a remainder of zero when divided by x – a, then x – a is a factor of p(x).

Example

State which of the following binomial is a factor of P(X), where

P(x) = x³+3x²-4x-12. Find:

1. X – 1      b)  X – 2

Solution

1. X – 1 = 0                                        b)  X – 2 = 0

X = 1                                                     X = 2

P(1) = 1³+3(1)²-4(1)-12                                 P(2) = 2³+3(2)²-4(2)-12

          = -12                                                               = 0

 ∴x-1 is not a factor of px     ∴x-2is a factor of p(x)

Since it has a remainder of -12