math review

Fundamental theorem of algebra

A polynomial function of degree n>0 has n complex zeros. Some of these zeros may be repeated.

Rational zeros theorem

The only possible rational zeros of a function are p/q, where p is a divisor of the constant term and a is a divisor of the leading coefficient.

The remainder theorem

If a polynomial is divided by (x-c), then the remainder is the same as the function value f(c )

Factor theorem

If c is a zero, then (x-c) is a factor and vice versa

Multiplicity

The number of times a zero or factor is repeated

Complex conjugate zeros

If x=a+bi is a zero of a polynomial, then x=a-bi (the conjugate) is also a zero

Factors of a polynomial with real coefficients

Every polynomial function with real coefficients can be written as a product of linear factors and irreducible quadratic factors*, each with real coefficients

*An irreducible quadratic factors is a quadratic with NO real solutions (I.e. 2 complex solutions)