Question

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

Answer 1

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