Remainder and factor theorems
If we divide a polynomial by (x − r), we obtain a result of the form:
f(x) = (x − r) q(x) + f(r)
where q(x) is a polynomial with one degree less than the degree of f(x) and f(r) is the remainder. This is called the remainder theorem.
If the remainder f(r) = 0, then (x − r) is a factor of f(x).
Is (x-2) a factor of f(x)=x3-2x-6?
We identify r as 2 and plug that value into our function:
(x-2) is not a factor of f(x)=x3-2x-6
Is (x-1) a factor of f(x)=x4-2x2+1?