how do I factor f(x)=x^3-x^2-4x+4 and find all the possible roots of f(x)

Question

how do I factor f(x)=x^3-x^2-4x+4 and find all the possible roots of f(x)

Answer 1

Our roots would be 2 , -2 and 1

 

We need to use synthetic division or long division to find all the roots of the above function.

 

Solution check:

 

f(2) = 8 - 4 - 8 + 4

 

= 0

 

f(-2) = -8 - 4 + 8  + 4

 

= 0

 

f(1) = 1-1-4+4

 

= 0

 

We just verified that all of the above were roots of the function given in the problem.