Question

Can you pease help me find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic devision?

Answer 1

        x^3    - 5x^2 +    6x  -  30

    |   1        - 5            6      - 30
    |
    |
 5 |              5             0        30
----------------------------------------------
    |   1         0             6         0  <------ the resiude is 0.

Resiude 0 means that the polynomial is divisible by x - 5, and that means the root is x = 5.

That is the only rooto because the quotient is x^2 + 6, which does not have real roots.

Answer: x = 5