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Factored form of X3 + 3x2 – 4x - 12

fitzmerl duron
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To factor out $x^3 + 3x^2 -4x - 12$, let's try thinking what might be its factors. Let's try $x+2$. If we divide $x^3 + 3x^2 -4x - 12$ by $x+2$, the quotient will be $x^2 + x -6$, remainder zero. If the reminder is zero when we divide a higher degree polynomial equation by a lower-degree polynomial equation, then this lower-degree polynomial equation is one of the factors of this higher-degree polynomial equation.

The factors of $x^3 + 3x^2 -4x - 12$ is $x^2 + x -6$ and $x+2$. But notice that the expression $x^2 + x -6$ can be factored out into $x+3$ and $x-2$. Therefore...the factored form of $x^3 + 3x^2 -4x - 12$ is $(x+3)(x-2)(x+2)$.

$$\color{green}{x^3 + 3x^2 -4x - 12 = (x+3)(x-2)(x+2)}$$

Alternate solutions are encouraged...

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