Question

what are the values of a and b so that the polynomial p(x)=ax^3+x^2-2x+b is exactly divisible by (x+1) as well as (x-1)

Answer 1

Step-by-step explanation:

f(1) and f(−a) both are equal to 0 by factor theorem.

∴ f(1)=1+2+a+b=0 and f(−a)=−a3+2a2−a2+b=0

∴ a+b=−3 and −a3+a2+b=0

Thus, on solving two equations we get, a=−1 and b=−2