Answer :
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
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