first of all, you can only have one x, so i replaced the second x with c, meaning a constant, b is also a constant

x²-bx-c = (x- )(x+ )

x²-bx+c = (x- )(x- )

x²+bx-c = (x+ )(x- )

x²+bx+c = (x+ )(x+ )

Here are the rules:

Multiplying two things of the same sign gives a positive sign for the result. that is, a positive number times a positive number gives a positive number and a negative number times a negative number also gives you a positive number

Multiplying two things of opposite sign gives a negative sign for the result. that is, multiplying a positive number by a negative number (or vice versa) give a negative number.

when factorizing, you want to make sure the two numbers you pick, when they multiply you get the constant and when you add them, you get the coefficient of x.

so for

x²-bx-c

we see the constant has a negative sign, so the two numbers we find must have opposite signs, so you get (x - *) and (x + *)

for x²-bx+c

we notice the constant has a positive sign, so we need the same sign for both numbers we find. (x + ) and (x + ) wont work, since the coefficient of x is negative (if we add two positive numbers the result is positive--always). so we have to have (x - ) and (x - )

for x²+bx-c

we need (x + ) and (x - ) since a negative times a positive gives a negative for the constant and a positive plus a negative gives a positive if the positive number is bigger for the coefficient of x

for x²+bx+c

we need (x + ) and (x + ) since a positive times a positive is positive for the constant and a positive plus a positive is positive for the coefficient of x