Find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic division. show all three lines of numbers. you!

Write the coeeficientes of the polynomial in order:

  | 1   - 5   6   - 30
  |
  |
  |


After some trials you probe with 5

   | 1   - 5       6     - 30
   |
   |
5 |        5      0       30

     1     0      6        0 < residue

Given that the residue is 0, 5 is a root.

The quotient is x^2 + 6 = 0, which does not have a real root.

Therefore, 5 is the only root. You can prove it by solving the polynomial x^2 + 6 = 0.