It states that “ a polynomial p(x), when divided by x – a, leaves a remainder R, where R= P(a).

The “a” in p(a) is obtained by solving the equation x – a = 0

Example

Find the remainders when the polynomial p(x) = 2x³+3x²-5x-2 is divided by;

1. X – 1     ii)  X + 2

Solution

1. X – 1 = 0                            ii)     X + 2 = 0

X = 1                                            X = -2

P(1) = 2(1)³+3(1)²-5(1)-2                     P(-2) = 2(-2)³+3(-2)²-5(-2)-2

         = - 2                                                         = 4

∴ R = -2                                                        ∴R=4