Question

Use the Remainder Theorem to determine which of the roots are roots of F(x). Show your work.

Polynomial: F(x)=x^3-x^2-4x+4
Roots: 1, -2, and 2.

Answer 1

Answer: x1=1 x2=-2 and x3=2

Explanation:

1st x1=1 is 1 of the roots , so

F(1)=1-1-4+4=0 - true

So lets divide x^3-x^2-4x+4 by (x-x1), i.e (x^3-x^2-4x+4) /(x-1)=(x^2-4)

x^2-4 can be factorized as (x-2)*(x+2)

So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)

So there are 3 dofferent roots:

x1=1 x2=-2 and x3=2