Question

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

Please help, thank you.

Answer 1

Look for the low-hanging fruits first
Descartes' Rule of Signs says there are no negative roots, so that narrows things down a bit.
x^3-5x^2+6x-30 = (x-5)(x^2+6)

There is a nice synthetic division calculator at
https://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

Answer 2

Thank you oobleck :)