polynomial in one variable
A polynomial that contains no more than one different variable
degree of a polynomial
the greatest degree of any term in the polynomial
leading coefficient
The coefficient of the term with the highest degree
polynomial function
a function that is represented by a polynomial equation
zeros of a function
Values of the variable for which the value of a function is zero. Also called roots of a function.
polynomial equation
a polynomial that is set equal to zero
imaginary number
the square root of a negative number
root of an equation
a solution of an equation
complex number
a number of the form a+bi where a and b are real numbers and i is the square root of -1
Fundamental Theorem of Algebra
Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers.
completing the square
a process used to make a quadratic expression into a perfect square trinomial
Quadratic Formula
x = -b � ?(b� - 4ac)/2a
discriminate of quadratic equation
b^2-4ac
Remainder Theorem
If a polynomial f(x) is divided by x-k, the remainder is r=f(k)
synthetic division
a method used to divide a polynomial by a binomial
Factor Theorem
The binomial x-r is a factor of the polynomial P(x) if and only if P(r)=0
depressed polynomial
the quotient when a polynomial is divided by one of its binomial factors
Rational Root Theorem
Identifies a list of possible zeroes of a polynomial function.
Integral Root Theorem
if the leading coefficient is one, then any rational roots must be factors of a sub n
Descartes' Rule of Signs
a technique for finding the number of positive and negative roots to a polynomial equation with real coefficients
location principle
A way of finding roots or zeros of a function
Upper Bound Theorem
Suppose c is a positive real number and P(x) is divided by x-c. If the resulting quotient and remainder have no change in sign then P(x) has no real zero greater than c. Thus c is an upper bound of the zeros of P(x)
upper bound
the highest value that a prediction is likely to be
lower bound
the lowest value that a prediction is likely to be