# How do you factor  x^3 +3 = x +3x^2?

May 6, 2016

Transpose the equation to have all the terms on one side, then factorise.

#### Explanation:

x^3 -3x^2 -x +3 = 0 ............. All the terms on one side in .......................................................descending powers of x

Common factor:

${x}^{2} \left(x - 3\right) + \left(- x + 3\right) = 0$ .................... grouping

${x}^{2} \left(x - 3\right) - \left(x - 3\right) = 0$ ......... switchround to make common brackets

$\left(x - 3\right) \left({x}^{2} - 1\right) = 0$.................common bracket

(x - 3)(x + 1)(x - 1) = 0 ........... difference of two squares

We were not asked to solve, only to factorise, but if we do solve the equation, the solutionswould be :

$x = 3 , x = - 1 , x = 1$