Question

Use factor theorem to show that;

(X-2) is a factor of the polynomial X³-X-6
(X+2)(X-1) is a factor of the polynomial
P(X)=X⁴+X³+2X²+4X²-8

Answer 1

let

f(x)=x³-x-6,

if (x-2) is a factor of f(x), then f(2) should be equal to zero,

then

f(2)=2³-2-6,

f(2)=8-8=0,

since

f(2)=0,

therefore (x-2) is a factor of f(x).