# Find the value of a for which the polynomial is divisible by (x+3).

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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