For finding whether or not ax^2+bx+c=0 can be factorized or not, we find the value b^2-4ac.
As the equation is x^2−x−56, b^2-4ac=1^2-4xx1xx(-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 x^2 and independent term into two factors, whose sum is b, the coefficient of x.
In the polynomial x^2−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
x^2−x−56=x^2−8x+7x−56 i.e.
x(x-8)+7(x-8) or
(x+7)(x-8)
