[tex]\displaystyle\\
a)~~~x^2-7x+12 =\\
~~=x^2-3x-4x+12=x(x-3)-4(x-3)=\boxed{(x-3)(x-4)}\\\\
b)~~~x^2-x-56 = \\
~~=x^2-8x+7x-56 = x(x-8)+7(x-8)=\boxed{(x-8)(x+7)}\\\\
c)~~~x^2-2x-24=\\
~~=x^2-6x+4x-24=x(x-6)+4(x-6)=\boxed{(x-6)(x+4)}\\\\
d)~~~x^2+8x+15=\\
~~=x^2+3x+5x+15=x(x+3)+5(x+3)=\boxed{(x+3)(x+5)}\\\\
e)~~~x^2-x-90= \\
~~=x^2-10x+9x-90=x(x-10)+9(x-10)=\boxed{(x-10)(x+9)}\\\\
f)~~~x^2-3x-70= \\
~~=x^2-10x+7x-70=x(x-10)+7(x-10)=\boxed{(x-10)(x+7)} [/tex]
