Because the #x^2# coefficient is #1# we know the coefficient for the #x# terms in the factor will also be #1#:
#(x )(x )#
Because the constant is a negative and the coefficient for the #x# term is a negative we know the sign for the constants in the factors will have one positive and one negative because a negative plus a positive can be a negative and negative times a positive is a negative:
#(x - )(x + )#
Now we need to determine the factors which multiply to 48 and when subtracted are -2:
#1 xx -48 = -48#; #1 - 48 = -47 # <- this is not the factor
#2 xx -24 = -48#; #2 - 24 = -22 # <- this is not the factor
#3 xx -16 = -48#; #3 - 16 = -13 # <- this is not the factor
#4 xx -12 = -48#; #4 - 12 = -8 # <- this is not the factor
#6 xx -8 = -48#; #6 - 8 = -2 # <- this IS the factor
#(x - 8)(x + 6)#
