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

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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# .................... grouping

#x^2(x - 3) - (x - 3) = 0# ......... switchround to make common brackets

#(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#