William W. answered • 09/30/20
Math and science made easy - learn from a retired engineer
The rational roots theorem tells us that if there are any rational roots, they will be plus or minus the factors of 6 divided by the factors of 3. That means they could be ± 1/3, 2/3, 1, 2, 3, 6. A lower bound will always be negative. Let's start by trying x = -1. So we use synthetic division for x = -1
The coefficients of the polynomial are -3, 0, 6, 2, -8, and 6 so we do synthetic division like this:
We do not see the characteristic minus/plus/minus/plus... in the quotient coefficients (bottom row). So we need to go lower. So lets try -2:
This DOES show the minus/plus/minus/plus characteristic so x = -2 is a lower bound. There will be no zeros smaller that -2.
