Question 982436: Use the Factor Theorem to determine whether the first polynomial is a factor of the second.
x + 2; x^8 + 2x^7 + x + 2 Answer by ikleyn(52863) (Show Source):
If a polynomial f(x) has the number x = a as the root, i.e. f(a) = 0, then the polynomial f(x) has the binomial x-a as the factor. In other words, the binomial x-a divides f(x) without a remainder.
In your case, in order to prove that has the binomial x+2 as the factor, you simply should to check that the number -2 is the root of this polynomial. It is easy to do. Simply substitute the number -2 into the polynomial and calculate the result.
