Answer :

Let, f(x) = x4 – x3 – 11x2 - x + a


Now, we have


x + 3 = 0


x = -3


Hence,


f(-3) = (-3)4 – (-3)3 – 11(-3)2 – (-3) + a


= 81 + 27 – 11 × 9 + 3 + a


= 81 + 27 – 99 + 3 + a


= 111 – 99 + a


= 12 + a


As per question,


(x + 3) is the factor of f(x)


Now, by using factor theorem we get


(x – a) will be the factor of f(x) if f(a) = 0 and hence f(-3) = 0


So,


f(-3) = 12 + a = 0


a = -12


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