Question

how do you find the factor of the polynomial x squared minus x minus 20

Answer 1

The factorization scheme that jumped to my mind when i looked at your polynomial was
( x - a )( x + b ) = x^2 - ax + bx - ab

Knowing that in your case we would need values for a and b such that
b - a = -1 and ab = 20. Since 20 = 4 * 5 and 4 - 5 = -1 we have a solution at
( x - 5 )( x + 4 ) = x^2 - x - 20
as required.

Does that help?