If \(x=1\) is root of the equation \(x^{3}-2 x^{2}-5 x+6\), find the other roots ____________
Explanation
If \(x=1\) is a root of the given equation, then \(x-1\) will divide the given equation without any remainder. To find other factors, we employ long division as shown below
\begin{array}{r}
\frac{x^{2}-x-6}{x-1 \sqrt{x^{3}-2 x^{2}-5 x+6}} \\
\frac{-x^{3}-x^{2}}{x^{2}-5 x+6} \\
\frac{-x^{2}+x}{-6 x+x} \\
\frac{-6 x+x}{}
\end{array}
we further factorise \(x^{2}-x-6\)
\(x^{2}-x-6=x^{2}-3 x+2 x-6\)
\(x(x-3)+2(x-3):(x+2)(x+3)\)actors, \(x+2=0 \quad x=-2\)
\(x-3=0 \quad x=3\)