math polynomial long division

upper bound

When a polynomial P(x) is divided by x-a, where a>0, if all the terms of the quotient are non-negative and the remainder is non-negative, then a is an upper bound of the zeros P

multipilicity

the number of times a particular value is a zero of a polynomial function

lower bound

when a polynomial P(x) is divided by x-a, where a<0, if the terms of the quotient and the remainder alternate in sign, then a is a lower bound of the zeros P

remainder theorem

when a polynomial p(x) is divided by x-a, the remainder is equal to p(a)

upper bound(short)

A value of x above which there are definetly no zeros

lower bound(short)

A value of x below which there are definetly no zeros

Fundamental Theorem of Algebra

Every polynomial function of positive degree with complex coefficients has at least one complex zero

The Sum of the Product of the Roots of a Quadratic Equation

The sum of the roots of a quadratic equation ax²+bx+c=0 is equal to -b/a, and the product of the equations root is equal to c/a

The Conjugate-Zeros Theorem

If p(x) is a polynomial w/real coefficients and if a+bi( where a and b are real and b does not equal 0) is a zero of P, then a-bi is also a zero of P

factor theorem

If the divided of the polynomial and P(a)=0, then x-a is a factor of P(x)

Pascal's Triangle

a pattern for finding the coefficients of the terms of a binomial expansion