How to factor the expression: x^3 - 3x^2 - 4x + 12

[Math_Junkie]

How do you factor the following expression?

x^3 - 3x^2 - 4x + 12

Is there a rule for these type of expressions? I have no idea how to start..

Any help will be greatly appreciated.

 

[galactus]

$\displaystyle x^{3}-3x^{2}-4x+12$

$\displaystyle (x^{3}-3x^{2})-(4x-12)$

$\displaystyle x^{2}(x-3)-4(x-3)$

$\displaystyle (x^{2}-4)(x-3)$

$\displaystyle (x+2)(x-2)(x-3)$

No fancy tricks. Just grouping and factoring.

But, some are tougher.Look up the Rational Root Theorem.