How to Solve This Cubic Equation Turned Out to Be A Special Case of Differences of Cubes and Squares

This Cubic Equation Turned Out to Be A Special Case Where You Can Apply The Difference of 2 Cubes and and Difference of Two Squares. The solution is indeed an elegant one.

[@marlydahl]

This can be easily solved using synthetic division but you took it to a whole 'nother level. Very nice tips and tricks.

[@learnmathbydoing]

Yes po, you are right. We just use this as an opportunity to share another method they can use in solving this problem

[@nasrullahhusnan2289]

By inspection x³+x²=12 can be written as x³+x²=2³+2². Hence x=2.
To find other root, if any, note that the last equation can be written as
x³-2³+x²-2²=0
(x-2)(x²+2x+4)+(x+2)(x-2)=0
(x-2)(x²+3x+4)=0
x=2, x=½[-6±isqrt(3)]
For real root x=2 is the only one. Other root is a complex one.