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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