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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