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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