For finding whether or not ax2+bx+c=0 can be factorized or not, we find the value b2−4ac.
As the equation is x2−x−56, b2−4ac=12−4×1×(−56)=1+224=225. As it is a perfect square, it should be possible to factorize it.
Hence for factorizing, we split ac (the product of coefficient of x2 and independent term into two factors, whose sum is b, the coefficient of x.
In the polynomial x2−x−56, the product is −56 and hence factors whose sum is −1, these would be −8 and 7. Hence splitting middle term this way, we get
x2−x−56=x2−8x+7x−56 i.e.
x(x−8)+7(x−8) or
(x+7)(x−8)
