Question

Given a polynomial f(x), if (x - 1) is a factor, what else must be true?

Answer 1

If (x-1) is a factor of f(x), f(x) can be written as (x-1)*g(x) where g(x) is another polynomial.

Answer 2

If x=1, you get f(1)=(1-1)*g(1)=0*g(1)=0
So, you get that f(1)=0 is true.

Answer 3

Just for bonus, if f(x) has (x-c) as its factor (c=constant), f(c)=0 is always true.

Answer 4

Thank you!

Answer 5

Better known as the Factor Theorem.