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Level 525

Polynomial Functions


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polynomial
A monomial or sum of monomials
Degree of a polynomial
the degree of the term in the polynomial that has the highest degree
Power (exponent)
The number of times you multiply a base by itself.
Zeros (of a function)
The roots or x-intercepts of a function.
Synthetic Division (process)
A method used to divide a polynomial by a binomial (x-k).
factor
A number that divides evenly into another number. 3 is a factor of 15 (look at the chart!)
Distribute (expand)
Multiply the number on the outside of the parenthesis with anything Inside the parenthesis.
complete the square
A method used to rewrite a quadratic in standard form into vertex form.
Quadratic Formula
x = -b±√b²−4ac / 2a
second degree- quadratic function
Name the degree and give the common name of the polynomial function.
Third degree - Cubic function
Name the degree and give the common name of the polynomial function.
Fourth degree _ quartic function
Name the degree and give the common name of the polynomial function.
Quartic Function
Name the degree and give the common name of the polynomial function.
Fifth degree - Quintic function
Name the degree and give the common name of the polynomial function.
sum of cubes
An expression of the form a^3 +b^3. It can be factored as (a + b) (a^2 - ab + b^2).
Difference of cubes
An expression of the form a^3 - b^3. It can be factored as (a - b) (a^2 + ab +b^2).
monomial
a number or a product of numbers and variables with exponents that are whole numbers
Degree of a monomial
the sum of the exponents of the variables
Polynomial function
The graph crosses the x-axis up to n times and has up to n - 1 vertices (points where the function changes direction). The domain is all real numbers.
Standard form of a polynomial function
It arranges the terms by degree in descending numerical order.
Turning point
Places where the graph changes direction.
End Behavior
Look at HA
Factor Theorem
A polynomial f(x) has a factor (x-c) if and only if f(x) = 0
Multiple zero
If a linear factor is repeated in the complete factored form of a polynomial, the zero related to that factor is a _____________________.
Multiplicity
The number of times the related linear factor is repeated in the factored form of the polynomial.
Relative maximum
The greatest value of the function at an up-to-down turning point.
Relative minimum
The lowest value of the function at a down-to-up turning point.
Synthetic division
To find a slant asymptote
Remainder Theorem
If a polynomial f(x) is divided by (x-c), the remainder is f(c)
Power function
The graph contains the origin if b is positive. In most real-world applications, the domain is nonnegative real numbers if b is positive and positive real numbers if b is negative.
Constant of proportionality
If y = ax^b describes y as a power function of x, then y varies directly with, or is proportional to, the nth power of x. The constant a is the:
Fundamental Theorem of Algebra
If P(x) is a polynomial of degree n>or equal to 1. then P(x)=0 has exactly n roots, including multiple and complex roots.
Expand
to expand the power of a bionmial, multiply as needed, then write the polynomial in standard form.
Pascal's triangle
any number is sum of the two numbers immediately above it