Algebra
Remainder & factor theorems
If P(a) = 0, then (x − a) is a factor. The fastest factor check there is.
Two related theorems for polynomials.
The theorems
- Remainder: when P(x) is divided by (x − a), the remainder is P(a).
- Factor: if P(a) = 0, then (x − a) is a factor of P(x).
Try it
Is (x − 2) a factor of x³ − 8?
P(2) = 8 − 8 = 0. Yes — it's a factor.