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Polynomial/Polynomial Function

Synthetic Substitution

End Behavior

Factor Completely

A polynomial is a monomial or a sum of monomials. A polynomia…

Another way to evaluate a polynomial function is to use synth…

The end behavior of a function's graph os the behavior of the…

A factorable polynomial with integer coefficients is factored…

Polynomial/Polynomial Function

A polynomial is a monomial or a sum of monomials. A polynomia…

Synthetic Substitution

Another way to evaluate a polynomial function is to use synth…

monomial

binomial

trinomial

polynomial

Any numeral, variable, or a product of a numeral and one or m…

A polynomial with two terms.

A polynomial with three terms.

A monomial or sum of terms that are monomials.

monomial

Any numeral, variable, or a product of a numeral and one or m…

binomial

A polynomial with two terms.

Degree of a Polynomial

Depressed Polynomial

End Behavior

Extrema

The highest degree in a polynomials

The result of dividing polynomials

What direction the graph is going

A maximum or minimum

Degree of a Polynomial

The highest degree in a polynomials

Depressed Polynomial

The result of dividing polynomials

algebraic expression

Equality Properties

numerical expression

solve

an expression that contains at least one variable

applying the same operation to both sides of an equation form…

an expression that contains only numbers and symbols

to work out a solution

algebraic expression

an expression that contains at least one variable

Equality Properties

applying the same operation to both sides of an equation form…

monomial

degree of a monomial

polynomial

degree of a polynomial

Is a real number, a variable, or a product of a real number a…

The degree of a monomial in one variable is the exponent of t…

a monomial or a sum of monomials

The degree of a polynomial in one variable is the greatest de…

monomial

Is a real number, a variable, or a product of a real number a…

degree of a monomial

The degree of a monomial in one variable is the exponent of t…

monomial

binomial

trinomial

polynomial

a real number, variable or product of a real number and one o…

two monomials connected with addition or subtraction... ex. 3x²+…

three monomials connected with addition or subtraction... ex. x⁴…

a monomial or a sum of monomials

monomial

a real number, variable or product of a real number and one o…

binomial

two monomials connected with addition or subtraction... ex. 3x²+…

Monomial

Degree of a Monomial

Degree of a Polynomial

Standard Form of a Polynomial Function

a real number, a variable, or a product of real numbers and v…

the exponent of a variable

the greatest degree among its monomial terms

terms are listed in descending order of degree, and like term…

Monomial

a real number, a variable, or a product of real numbers and v…

Degree of a Monomial

the exponent of a variable

monomial

degree of a monomial

polynomial

polynomial function

Is a real number, a variable, or a product of a real number a…

The degree of a monomial in one variable is the exponent of t…

a monomial or a sum of monomials

...

monomial

Is a real number, a variable, or a product of a real number a…

degree of a monomial

The degree of a monomial in one variable is the exponent of t…

Varible

Algebraic expression

Coefficient

Define a variable

A symbol that represents an unknown quantity

An expression that contains variables,numbers,and at least on…

The numerical factor of a multiplication expression that cont…

When you choose a variable to represent an unknown quantity

Varible

A symbol that represents an unknown quantity

Algebraic expression

An expression that contains variables,numbers,and at least on…

Monomial

degree of a monomial

Polynomial

Standard form of a polynomial

A real number, a variable, or a product of a real number and…

The sum of the exponents of the variables of a monomial.

A monomial or the sum or difference of two or more monomials.…

The form of a polynomial that places the terms in descending…

Monomial

A real number, a variable, or a product of a real number and…

degree of a monomial

The sum of the exponents of the variables of a monomial.

polynomial

degree

like terms

GCF

one or more terms

______ of a monomial --> If a ≠ 0, the degree of axn is n. Th…

Terms that have the same variables AND the same... exponents.

greatest common factor

polynomial

one or more terms

degree

______ of a monomial --> If a ≠ 0, the degree of axn is n. Th…

Order of Operations

Variable

Evaluate

Expression

1st - (Parenthesis) ... 2nd - Multiply & Divide ... 3rd - Add & Sub…

Unknown, represented by a number

Solve

a number or group of numbers with operation symbols

Order of Operations

1st - (Parenthesis) ... 2nd - Multiply & Divide ... 3rd - Add & Sub…

Variable

Unknown, represented by a number

Point slope form

Converse

Parallel Lines

Perpendicular

The point slope form of the equation of the non vertical line…

The converse of a conditional statement interchanges the hypo…

If two non vertical lines in the same plane have the same slo…

Two lines in the same plane are perpendicular if they interse…

Point slope form

The point slope form of the equation of the non vertical line…

Converse

The converse of a conditional statement interchanges the hypo…

Define monomial

What is an example of a monomial?

What is the degree of a monomial? (in…

What is a polynomial?

a real number, variable, or product of a real number and one…

y = 16

the exponent of the variable

a monomial or sum of monomials

Define monomial

a real number, variable, or product of a real number and one…

What is an example of a monomial?

y = 16

algebraic expression

Equality Properties

numerical expression

solve

an expression that contains at least one variable

applying the same operation to both sides of an equation form…

an expression that contains only numbers and symbols

to work out a solution

algebraic expression

an expression that contains at least one variable

Equality Properties

applying the same operation to both sides of an equation form…

Algebra

Term

Polynomial

Monomial

a branch of mathematics that uses symbols to represent unknow…

an expression formed from the product of numbers and or varia…

an algebraic expression made up of terms connected by the ope…

an algebraic expression with ONE term. 6y

Algebra

a branch of mathematics that uses symbols to represent unknow…

Term

an expression formed from the product of numbers and or varia…

polynomial

term

coefficient

monomial

the sum of powers in one or more variables multiplied by coef…

Within a polynomial, each product

the number being multiplied by a power

Polynomials with only one term

polynomial

the sum of powers in one or more variables multiplied by coef…

term

Within a polynomial, each product

Positive Integral Exponents

Negative Integral Exponents

Zero Exponent

Product Rule of Exponents

If x is a nonzero real number, and n is a positive integer, t…

If x is a nonzero real number, and n is a negative integer, t…

If a is any nonzero real number, then a⁰=1

If m and n are integers, and a=0, then aᵐ × aⁿ = aᵐ⁺ⁿ

Positive Integral Exponents

If x is a nonzero real number, and n is a positive integer, t…

Negative Integral Exponents

If x is a nonzero real number, and n is a negative integer, t…

Variable

Algebraic expression

Algebra tiles

Power

A quantity whose value can change, usually represented by a l…

A mathematical phrase made up of numbers and variables, conne…

We can use different tiles to respire sent expressions, shade…

A product of identical factors and consists of two parts, the…

Variable

A quantity whose value can change, usually represented by a l…

Algebraic expression

A mathematical phrase made up of numbers and variables, conne…

Products of Exponents... Product of Powers

Products of Exponents... Power of a Power

Products of Exponents... Power of a Product

Products of Exponents... Negative Exponent

a ⁿ ₀ aⁿ = a ⁿ⁺ⁿ

(a ⁿ )ⁿ = a ⁿⁿ

(ab) ⁿ = a ⁿb ⁿ

a⁻ⁿ = 1/aⁿ , a ≠ 0

Products of Exponents... Product of Powers

a ⁿ ₀ aⁿ = a ⁿ⁺ⁿ

Products of Exponents... Power of a Power

(a ⁿ )ⁿ = a ⁿⁿ

monomial

degree of a monomial

polynomial

degree of a polynomial

A polynomial with one term

The exponent of the variable (3x^2 -> degree = 2)

A monomial or sum of monomials

The highest exponent of a variable in the polynomial

monomial

A polynomial with one term

degree of a monomial

The exponent of the variable (3x^2 -> degree = 2)

Monomial

Constant

Coefficient

Polynomial

A numeral, a variable, or the product of a numeral and one or…

A monomial that contains no variables

The numerical factor of a monomial

A monomial or the sum of monomials

Monomial

A numeral, a variable, or the product of a numeral and one or…

Constant

A monomial that contains no variables

End behavior

Local Maximum

Local Minimum

Zeros

Describes the direction of the y-values as x goes to positive…

A peak in the y-values of the graph of the function, but not…

A low in the y-values of the graph of the function, but not t…

Where the graph of the function touches or crosses the y-axis.

End behavior

Describes the direction of the y-values as x goes to positive…

Local Maximum

A peak in the y-values of the graph of the function, but not…

polynomial

factoring

conjugates

SOPPS

a finite sum of terms in which all variables are raised to wh…

writing a polynomial as a product

(a - b) and (a + b)... only the second sign is opposite

acronym for factoring sum/diff of cubes... *S*quare... *O*pposite *…

polynomial

a finite sum of terms in which all variables are raised to wh…

factoring

writing a polynomial as a product

polynomial

polynomial function

synthetic substitution

end behavior

a monomial or a sum of monomials

a function of the form... the exponents are all whole numbers…

a method used to evaluate a polynomial function

the behavior of the graph of a function as x approaches posit…

polynomial

a monomial or a sum of monomials

polynomial function

a function of the form... the exponents are all whole numbers…

Scientific Notation

Polynomial

Polynomial Function

End Behavior

A number in the form c x 10^n, where c is between 1 and 10, a…

A monomial or sum of monomials.

The behavior of the graph as x approaches positive infinity o…

Scientific Notation

A number in the form c x 10^n, where c is between 1 and 10, a…

Polynomial

A monomial or sum of monomials.

Binomial

Coefficient

complex conjugates

complex numbers

A polynomial equation with 2 terms

A number multiplied by a variable in an algebraic expression.

Opposites of your complex number Ex: (a+bi) and (a-bi)

They are often represented as A + Bi.

Binomial

A polynomial equation with 2 terms

Coefficient

A number multiplied by a variable in an algebraic expression.

end behavior

monomial

multiplicity

Pascal's Triangle

describes the directions of the graph as you move to the left…

either a real number, a variable, or the product of real numb…

the number of times the related linear factor is repeated in…

a triangular array of numbers in which the first and last num…

end behavior

describes the directions of the graph as you move to the left…

monomial

either a real number, a variable, or the product of real numb…

Monomial

degree

polynomial

Standard form of a polynomial

expression that is a number, a variable or a product of a num…

exponent

any monomial or the sum/difference of two or more monomials

written from greatest to least degree

Monomial

expression that is a number, a variable or a product of a num…

degree

exponent

The Product Rule

Zero Exponent

The Quotient Rule

Negative Exponents

When multiplying with like bases, the exponents are added tog…

Anything with a zero exponent equals 1.

When dividing with like bases, the exponents are subtracted.

If a variable has a negative exponent, it is moved to the oth…

The Product Rule

When multiplying with like bases, the exponents are added tog…

Zero Exponent

Anything with a zero exponent equals 1.

In 5.1: what does B and M equal

Parallel Line:... what equation:

how to find the slope with two points

perpendicular lines... PROVE

B= starting point... M= rate of change

same slope... y=mx+b

y2-y1... x2-x1

their slopes are negative reciprocals of each others ... WRITE A…

In 5.1: what does B and M equal

B= starting point... M= rate of change

Parallel Line:... what equation:

same slope... y=mx+b

when multiplying two numbers with expo…

when a number with an exponent has an…

when two variables are being multiplie…

when the same variable with different…

multiply numbers and add exponents... x^m+n

multiply exponents... x^mn

multiply the variables by the exponent... x^m y^m

subtract the exponents... x^m-n

when multiplying two numbers with expo…

multiply numbers and add exponents... x^m+n

when a number with an exponent has an…

multiply exponents... x^mn

Rate of change

Slope

Direct variation

Parent function

Change of the depentant variable... ____________________________…

Vertical change Rise... ____________________ = _____... Horizontal…

Described by any equation in the form Y=KX

The simplest function from the basic set of functions. Y=X or…

Rate of change

Change of the depentant variable... ____________________________…

Slope

Vertical change Rise... ____________________ = _____... Horizontal…

binomial

degree of a monomial

degree of a polynomial

difference of two squares

a polynomial of two terms

is the sum of the exponents of its variables

is the highest degree of any term in the polynomial

an expression of the form a^2 - b^2. It can be factored as (a…

binomial

a polynomial of two terms

degree of a monomial

is the sum of the exponents of its variables

degree of a monomial

end behavior

monomial

multiplicity

the sum of the exponents of all variables in the one term

the directions of the graph to the far left or far right

a number, a variable, or a product of a number and one or mor…

the number of times that a variable's associated factor appea…

degree of a monomial

the sum of the exponents of all variables in the one term

end behavior

the directions of the graph to the far left or far right

polynomial

monomials

1 term

2 terms

A sum and or difference of one or more monomial.

a term made of the product of one or more contants and/or var…

monomial ex: 3x

binomial ex: 5x(2)=7

polynomial

A sum and or difference of one or more monomial.

monomials

a term made of the product of one or more contants and/or var…

Remainder Theorem

Factor Theorem

Multiple Zero

Multiplicity

A remainder of 0 tells us that the DIVISOR is a factor of the…

Factors, roots, zeros, x-intercepts, & solutions are all inte…

Solution that counts as more than one zero

The number of times a MULTIPLE ZERO counts

Remainder Theorem

A remainder of 0 tells us that the DIVISOR is a factor of the…

Factor Theorem

Factors, roots, zeros, x-intercepts, & solutions are all inte…

numerical expressions

algebraic expressions

order of operations

variable

These are combinations of numbers and operations

These are combinations of numbers, variables, and operations

This tells you which operation to perform first

A symbol, usually a letter, used to represent a number

numerical expressions

These are combinations of numbers and operations

algebraic expressions

These are combinations of numbers, variables, and operations

inequality

set-builder notation

compound inequality

intersection

An open sentence that contains the symbol <, ≤, >, ≥.

A concise way of writing a solution set. For example, {t ｜t <…

A ______________ containing 'and' is true if both of the ineq…

The graph of a compound inequality containing 'and' is the __…

inequality

An open sentence that contains the symbol <, ≤, >, ≥.

set-builder notation

A concise way of writing a solution set. For example, {t ｜t <…

5-1... Sales Tax

5-1... Domain

5-1... Piecewise Function

5-1... Split Function

tax paid when buying a used car

set of values that can be put into a function

gives set of rules for each domain of the function

piecewise function... - a function that gives a set of rules for…

5-1... Sales Tax

tax paid when buying a used car

5-1... Domain

set of values that can be put into a function