Question

3. Given the function f(x)=2x^4-4x^2+4x-8
a. Use the rational root theorem to list all possible rational roots
b. Use Descartes Rule of Signs to determine the number of positive and negative zeros

4. Use the remainder theorem and synthetic division to find the remainder when
f(x) = x^3-5x^2-11x+8 is divided by (x + 2)

Answer 1

#3 what about the theorems do you not understand?
(b) changes of sign of f(x) = 3, so there are 1 or 3 positive roots
There is only 1 change of sign of f(-x) = 2x^4-4x^2-4x-8, so there is exactly 1 negative root

#4. the lousy text formatting provisions here make it hard to show synthetic division, but there are several handy calculators online.

The Remainder Theorem says that the remainder will be f(-2) = 2