Question

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

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)