Question

• Find all roots of x^3-2x^2-5x+6

Answer 1

x^3-2x^2-5x+6=0; x=1 is an obvious root because the expression becomes just the sum of the coefficients: 1-2-5+6=0. That means we can divide by this root using synthetic division and then we have a quadratic which should be easy to solve. 

1 | 1 -2 -5...6

.....1..1 -1..-6

.....1 -1 -6 | 0

Quadratic is x^2-x-6=(x-3)(x+2)=0, so x=3, -2 and the root we found earlier 1.

x^3-2x^2-5x+6=(x-1)(x-3)(x+2).