唔識做功課40

Since the remainder is - 1 and - 5 when F(x) is divided by x - 1 and x + 1,
F(1) = - 1 and F(- 1) = - 5F(x) = Q(x) (x - 1) (x + 1) + ax + b where Q(x) is the quotient.F(1) = Q(1) (1 - 1) (1 + 1) + a(1) + b
{
F(- 1) = Q(- 1) (- 1 - 1) (- 1 + 1) + a(- 1) + b - 1 = a + b
{
- 5 = - a + bSolving, a = 2 and b = - 3
∴ The remainder is 2x - 3.