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Question

Find the value of a for which the polynomial (x4 − x3 − 11x2 − x + a) is divisible by (x + 3).

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Solution

Let:
fx=x4-x3-11x2-x+a
Now,
x+3=0x=-3
By the factor theorem, fx is exactly divisible by x+3 if f-3=0.
Thus, we have:
f-3=-34--33-11×-32--3+a =81+27-99+3+a =12+a
Also,
f-3=012+a=0a=-12
Hence, fx is exactly divisible by x+3 when a is -12.

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