List all possible rational zeros for the given function. f(x) = 2x^3 - 3 x^2 - x + 1

Question

Answer:____?___

 

Use synthetic division to test the possible rational zeros and find an actual zero.
The rational zero you found is x = ____?_____

 

Now use your quotient from the synthetic division to find the remaining zeros of the polynomial function.
The remaining zeros of f(x) are x =___?___ and x =___?____

Answer 1

Possible rational zeros are ±1, ±½.

 

It's obvious that neither -1 nor 1 is going to work.  So let's divide (synthetically) by ½:

 

½| 2 -3  -1  1

         1  -1 -1

      2 -2 -2  0   ⇐Success!

 

The depressed polynomial is 2x² - 2x -2 and if we set this to zero we can find its zeros (roots) by the quadratic formula.  I will leave that to you.