Question

How to write a third degree polynomial with x-1 factor?

Answer 1

Let the other factors be (x-a)and (x-b)
The third degree polynomial p(x)=
(x-1)(x-a)(x-b)
=
$(x - 1)( { x}^{2} - ax - bx + ab) \\ {x}^{3} - a {x}^{2} - b {x}^{2} + abx - {x}^{2} + ax + bx - ab$
This is the required third degree polynomial.