24 terms

# Ch 5: Polynomials and Polynomial Functions Part A & B

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Monomial
Is a real number, a variable, or a product of a real number and one or more variables with whole-exponents.
Degree of a Monomial
Is one variable in the exponent of the variable.
Polynomial
Is a monomial or a sum of monomials.
Degree of a Polynomial
In one variable is the greatest degree among its monomial terms.
Polynomial Function
A polynomial with the variable x.
Standard form of a polynomial function
Arranges the terms by degree in descending numerical order.
Turning Point
Places where the graph changes direction.
End Behavior
The directions of the graph to the far left and to the far right.
Factor Theorem
The expression x - a is a linear factor of a polynomial if and only if the value of a root of the related polynomial function.
Multiple Zero
If a linear factor is repeated in the complete factored form of a polynomial, the zero related to that factor is a multiple zero.
Multiplicity
Is the number of times the related linear factor is repeated in the factored form of the polynomial.
Relative Maximum
Is the value of the function at an up-to-down turning point.
Relative Minimum
Is the value of the function at a down-to-up turning point.
Sum of Cubes
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Difference of Cubes
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Synthetic Division
Simplifies the long-division process for dividing by a linear expression x - a.
Remainder Theorem
Provides a quick way to find the remainder of a polynomial long-division problem.
Rational Root Theorem
Limited number of possible roots.
Fundamental Theorem of algebra
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Expand
The power of a binomial in general.
Pascals Triangle
Is a triangular array of numbers in which the first and last number of each row is 1.
Binomial Theorem
Gives a general formula for expanding a binomial.
Power Function
Is a function where a and b are nonzero real numbers.
Constant of Proportionality
The constant a in the power function.