SOLUTION: Use the Rational Zero Test to list all possible rational zeros of f. Verify that the zeros of f shown on the graph are contained in the list. f(x)=x^3-4x^2-4x+16

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Rational Zero Test to list all possible rational zeros of f. Verify that the zeros of f shown on the graph are contained in the list. f(x)=x^3-4x^2-4x+16       Log On


   

Question 448546: Use the Rational Zero Test to list all possible rational zeros of f. Verify that the zeros of f shown on the graph are contained in the list.
f(x)=x^3-4x^2-4x+16
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

rational roots of the equation 

 x^3-4x^2-4x+16=0   |If x = 2  then 8-16-8+16= 0

 x^3-4x^2-4x+16)/(x-2) = x^2-3x-10

 (x-2)(x^2-2x-8) = 0

factoring further

 (x-2)(x-4)(x+2) = 0   Rational roots: 2,4,-2