Question

3x^3-9x^2-31x+5=0

How do I find the zeros, using synthetic division

Answer 1

let f(x) = 3x^3-9x^2-31x+5
f(1) = 3 - 9 - 31 + 5 ≠ 0
f(-1) ≠ 0
f(5) = 375 - 225 - 155 + 5 = 0
so x = 5 , and x-5 is a factor

I assume you know how to perform synthetic division.

You should get (x-5)(3x^2 + 6x - 1)

This quadratic produces two more zeros, use the quadratic formula to find them

Answer 2

There is a nice online calculator at

https://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

It will show the steps involved.