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Question

If (x-1)^3
is a factor of  x^4+αx^3+βx^2+γx-1
then the other factor will be:

  1. x+1
  2. x-3
  3. x+2
  4. x
Answer

Let (x+p) be one of the factors.

(x-1)^3(x+p) = x^4+αx^3+βx^2+γx-1

x^4+x^3(p-3)+x^2(3-3p)+x(p-1)-p= x^4+αx^3+βx^2+γx-1

On comparing constant terms,

-p=-1

p=1

So, (x+1) is one of the factors.

Answer (A) – (x+1)

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