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