Factor and remainder theorems
Two related theorems for polynomials.
Factor theorem. is a factor of if and only if .
Remainder theorem. When is divided by , the REMAINDER equals .
The factor theorem is a special case of the remainder theorem (where the remainder is ).
Why useful. Lets you find roots without actually dividing — just SUBSTITUTE.
How to use to find . If the question says ' is a factor of ', set and solve for the unknown coefficient.
Cambridge tip. Match the sign carefully: , .
- Factor: factor iff .
- Remainder: dividing by gives remainder .
- Sign: .