maths

g(1) = (1 - a)(1 - b)(1 + 1) - 3 = 1
2(1 - a)(1 - b) = 4
(1 - a)(1 - b) = 4/2
[-(a - 1)][-(b - 1)] = 2
(a - 1)(b - 1) = 2
Since a<b, a and b are integers,
a - 1 = 1
b - 1 = 2
(Consider the factor of 2: 2 = 1 x 2 only this possible)
a = 2 and b = 3
Hence, g(x) = (x - 2)(x - 3)(x + 1) - 3
Since g(3) = -3
x - k, which equals x - 3, is not a factor of g(x).