Given :
[tex](x-12)(x+2)[/tex]The result will be :
[tex]\begin{gathered} (x-12)\cdot(x+2) \\ =x\cdot(x+2)-12\cdot(x+2) \\ =x^2+2x-12x-24 \\ =x^2-10x-24 \end{gathered}[/tex]So, (x-12)(x+2) is not a correct factorization of x^2 + 10x-24 because the result is
x^2 - 10x - 24
