x^2 – a^2 is called a difference of squares. Assuming one factor (the divisor) is (x – a), show by polynomial division that the other factor is (x + a)

(x^2-a^2)/(x-a)=(x+a)(x-a)/(x-a)=x+a.

(x+a)(x-a) = x^2-a^2).
This should be done by long division,
but it is difficult to show here.