a. $x^{2}-8x-9= x^{2}-8x+16-25= (x-4)^{2} - 5^{2}= (x-4-5).(x-4+5)= ( x-9).(x+1)$
b. $3x^2 - 5x -2 ^{}= 3x^{2}+x-6x-2 = (3x^{2}+x)-(6x+2)= x(3x+1)-2(3x+1)= (3x+1).(x-2)$
c. $x^{2}-x-6= x^{2} - 2.1.$ $\frac{1}{2}.x + $ ($\frac{1}{2})^{2}-$ $\frac{25}{4}= ( x- $ $\frac{1}{2})^{2}-($ $\frac{5}{2})^{2}= (x-$ $\frac{1}{2}-$ $\frac{5}{2}).(x-$ $\frac{1}{2}+$ $\frac{5}{2})= (x - 3).(x + 2) $
d. $4x^2 -36x + 56^{}= (2x)^{2}-2.2x.9+9^{2}-25=( 2x-9)^{2} - 5^{2} = ( 2x - 9 - 5 ).(2x - 9 + 5)= (2x -14) .(2x -4) $
