Question

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

Please show all three lines of numbers.

Thank you!

Answer 1

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.