Question

find all real solutions to the equation.
$x^3 - 4x^2 - 3x + 12 = 0$

Explanation:

Step1: Group polynomial terms

$(x^3 - 4x^2) + (-3x + 12) = 0$

Step2: Factor out common terms

$x^2(x - 4) - 3(x - 4) = 0$

Step3: Factor out binomial

$(x^2 - 3)(x - 4) = 0$

Step4: Set each factor to 0

$x^2 - 3 = 0$; $x - 4 = 0$

Step5: Solve for $x$

From $x-4=0$: $x=4$
From $x^2=3$: $x=\sqrt{3}$, $x=-\sqrt{3}$

Answer:

$x=4$, $x=\sqrt{3}$, $x=-\sqrt{3}$