124. Find the values of a and b so that (x + 1) and (x - 1) are factors of x⁴ + ax³ - 3x² + 2x + b.  

Let p (x) = x⁴ + ax³ - 3x² + 2x + b
If (x + 1) and (x - 1) are factors of p(x), then by factor theorem,
p(-1) = 0 ...(1) | x + 1 = 0 ⇒ x = -1
and    p(1) = 0 ...(2) | x - 1 = 0 ⇒ x = 1
Now,
P(-1) = 0
⇒ (-1)⁴ + a(-1)³ - 3(-1)² + 2 (-1) + b = 0
⇒ 1 - a - 3 - 2 + b = 0
⇒    -a + b = 4    ...(3)
and    p(1) = 0
⇒ (1)⁴ + a(1)³ - 3(1)² + 2 (1) + b = 0
⇒ 1 + a - 3 + 2 + b = 0
⇒    a + b = 0    ...(4)
Solving (3) and (4), we get
a = -2,b = 2