**
Conjugate Zeros Theorem
** -
If *P*(*x*) is a polynomial with real coefficients, and if *a* + *bi* is a zero of
*P*, then *a* - *bi* is a zero of *P*.

**
Factor Theorem
** -
If *P*(*x*) is a polynomial and *P*(*a*) = 0, then *x* - *a* is a factor of *P*(*x*).
In other words, if the remainder when *P*(*x*) is divided by *x* - *a* is 0, then
*x* - *a* is a factor of *P*(*x*).

**
Fundamental Theorem of Algebra
** -
Every polynomial function of positive degree with complex coefficients has at
least one complex zero.

*Corollary.* Every polynomial function of positive degree *n* has exactly
*n* complex zeros (counting multiplicities).

**
Multiplicity
** -
A function with *n* identical roots is said to have a zero of multiplicity
*n*.

**
Nested Form
** -
The form of a polynomial *P*(*x*) = (((((*a*)*x* + *b*)*x* + *c*)*x* + *d* )*x* + ^{ ... }).

**
Rational Zeros Theorem
** -
If

*P*(*x*) is a polynomial with integer coefficients and if

is a
zero of

*P*(*x*) (if

*P*() = 0), then

*p* is a factor of the constant
term of

*P*(*x*) and

*q* is a factor of the leading
coefficient of

*P*(*x*).

**
Remainder Theorem
** -
When a polynomial *P*(*x*) is divided by *x* - *a*, the remainder is equal to
*P*(*a*).

**
Root
** -
A number that, when plugged in for the variable, sets a function equal to zero.
Also called a *zero.*

**
Synthetic Division
** -
A process by which a polynomial is divided by a binomial, in which the
coefficients of the polynomial are placed in a row and multiplied by and added
to the constant divisor as in nested form.

**
Zero
** -
A number that, when plugged in for the variable, sets a function equal to zero.
Also called a *root.*