For each polynomial function,

a) find the rational zeros and then the other zeros; that is, solve f (x) = 0; and

b) factor f (x) into linear factors.

1) f (x) = x^3-4x^2+2x+4

f (x) = x^3-4x^2+2x+4, we know that f (2) = 8-16+4+4=16-16=0

and we can write f (x) = (x-2) Q (x) so Q (x) = f (x) / (x-2) = x²-2x-2

x²-2x-2=0 delta = (-1) ² - (1). (-2) = 1+2=3

x=1-sqrt3 or x=1+sqrt3

finally the zeros are x=2, x=1-sqrt3 or x=1+sqrt3