If (x + 1) and (x – 1) are factors of p (x) = ax³ + x² – 2x + b, find the values of a and b.

We have,

p (x) = ax³ + x² – 2x + b

It is given in the question that,

(x + 1) and (x – 1) are the factors of p (x)

∴ p (-1) = p (1)

So, p (-1) = a (-1)³ + (-1)² – 2 (-1) + b

0 = - a + 1 + 2 + b

0 = - a + 3 + b (i)

Also, p (1) = a (1)³ + (1)² – 2 (1) + b

0 = a + 1 – 2 + b

0 = a + b – 1 (ii)

As, p (-1) = p (1)

- a + 3 + b = a + b - 1

- 2a = - 4

a = 2

Now, putting the value of a in (ii), we get:

2 + b – 1 = 0

1 + b = 0

b = - 1

Hence, the value of a is 2 and that of b is -1