Question

find all real values of x such that f (x) = x^3-x^2-4x+4=0

Answer 1

Hey Aj :)

Answer 2

\[\Large\rm x^3-x^2-4x\color{orangered}{+4}=0\]By the Rational Root Theorem:
Since the leading coefficient is just 1, we can get one of our roots from the factors of positive 4.

Answer 3

So our roots will come from this selection of 6 numbers: \(\Large\rm \pm1,\pm2,\pm4\)
These are the possible integer factors of 4.

-1 x 4,
1 x -4,
2 x 2,
-2 x -2,

All of those numbers, yah?

Answer 4

For a cubic, we just want to plug the numbers in to find our first root.
Let's start with something nice and easy and see if it works or not.
x=1