Answer :

[tex]a^{2} + 10a - 24[/tex]

[tex]= (a - 2)(a+12)[/tex]


Note :
Remember this formulas :
[tex]x^{2} +bx+c = (x+p)(x+q)[/tex]

when :
[tex]p \cdot q = c\,\,\,\,\,\,and\,\,\,\,\,\,p+q =b[/tex]

[tex]a^2 + 10a - 24=\\ a^2-2a+12a-24=\\ a(a-2)+12(a-2)=\\ (a+12)(a-2)[/tex]