Question

Factor completely the polynomial or indicate that the polynomial is not factorable using integers.
x^2 - (y - 6) ^2

Answer 1

The polynomial you have posted is a difference of squares:

a^2 - b^2 = (a + b)(a - b)

In this case, a = x and b = y - 6 so

x^2 - (y - 6)^2 = (x + (y - 6))(x - (y - 6))
= (x + y - 6)(x - y + 6)

Answer 2

how do you determine the positive and negatives?

Answer 3

It's just using the formula and applying algebra