One factor of f(x)=4x^3-4x^2-16x+16 is (x – 2). what are all the roots of the function? use the remainder theorem.

The roots of f(x) are x=2, 1, -2

Step-by-step explanation:

Given polynomial is

One factor of above polynomial is (x – 2). we have to find all the roots of above polynomial. By applying synthetic division we find the quotient of above polynomial when divided by (x-2).

We get the coefficient

Hence, by remainder theorem,

                                               =

                                               =

                                               =

                                               =

To find roots, f(x)=0

⇒

⇒ x=2, 1, -2

3 4 7 12 19

+1 +3 +5 +6

i would guess 26 because this isnt a sequential pattern or its to short to know

(hint): the answer is in the question.