1. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the
real numbers. f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1
Solution
zero's =1,+ i/3,_i/3
OR x=1,1,-i/3,i/3
f ' (x) = 12x^2 + 6x - 6
Find Critical Values:
0 = 12x^2 + 6x - 6
0 = 6(2x^2 + x - 1)
0 = 6(2x - 1)(x + 1)
x = 1/2, -1
Intervals:
(-infinity, -1)----positive----increasing
(-1, 1/2)----------negative--decreasing
(1/2, infinity)----positive---increasing