Find the number a such that x-1 is a factor of x^3+ax^2-x+8
Use the polynomial remainder theorem.
Also, you could use Vieta's theorem.
When you have: , you know that:
... where are roots of .
So when you have and you know that 1 is root ( ), you can write three equations:
... so you have 3 equations with three unknowns, and you can solve for .