How do you factor $x^{3} + 3 = x + 3 x^{2}$ $x^3 +3 = x +3x^2$ ?

Question

1027 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-06T23:14:14

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

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

Common factor:

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

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

$(x - 3) (x^{2} - 1) = 0$ $(x - 3)(x^2 - 1) = 0$ .................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 :

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

How do you factor x3+3=x+3x2 x^3 +3 = x +3x^2?