Question 194722
Since we want {{{3x^2-k}}} to factor to {{{3(x-2)(x+2)}}}, this means that we want {{{3x^2-k=3(x-2)(x+2)}}}



{{{3x^2-k=3(x-2)(x+2)}}} Start with the given equation.



{{{3x^2-k=3(x^2+2x-2x-4)}}} FOIL



{{{3x^2-k=3(x^2-4)}}} Combine like terms.
 


{{{3x^2-k=3x^2-12}}} Distribute



{{{-k=-12}}} Subtract {{{3x^2}}} from both sides.



{{{k=12}}} Divide both sides by -1 to isolate "k".



So the solution is {{{k=12}}} which means that {{{3x^2-12}}} factors to {{{3(x-2)(x+2)}}}