## Quick Reference

The following result about polynomials:

Theorem

If a polynomial *f*(*x*) is divided by *x*−*h*, then the remainder is equal to *f*(*h*).

It is proved as follows. Divide the polynomial *f*(*x*) by *x*−*h* to get a quotient *q*(*x*) and a remainder which will be a constant, *r*. This means that *f*(*x*)=(*x*−*h*)*q*(*x*)+*r*. Replacing *x* by *h* in this equation gives *r*=*f*(*h*), thus proving the theorem. An important consequence of the Remainder Theorem is the Factor Theorem.

*Subjects:*
Mathematics.