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Monomial in Simplified Form has:

Degree of a Polynomial

Dividend

Divisor

No powers of powers... Each base appears exactly once... All fracti…

Highest exponent in the Polynomial

Number inside the division symbol. The divisor goes into it.

Number on left of the division symbol. It goes into the divid…

Monomial in Simplified Form has:

No powers of powers... Each base appears exactly once... All fracti…

Degree of a Polynomial

Highest exponent in the Polynomial

Algebraic expression

Binomial

Coefficient

Common difference

contains numbers, variables, and operations (no equal sign)

an expression that contains two terms

the "big" number in front of the variable

the constant difference between consecutive terms in a sequence

Algebraic expression

contains numbers, variables, and operations (no equal sign)

Binomial

an expression that contains two terms

Monomial

Degree of a Monomial

Polynomial

Degree of a Polynomial

a number, variable or the product of a number and one more va…

the sum of the exponents of the variables in the monomial... 3a…

a monomial or sum of monomials -- each called a term or the p…

the greatest degree in its term... 3ab² + b = Degree: 3

Monomial

a number, variable or the product of a number and one more va…

Degree of a Monomial

the sum of the exponents of the variables in the monomial... 3a…

term

standard form

coefficient

greatest common factor (GCF)

a single number or variable

a way of writing down very large or very small numbers easily

a numerical or constant quantity placed before and multiplyin…

the greatest factor that divides two numbers

term

a single number or variable

standard form

a way of writing down very large or very small numbers easily

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.

Monomial

Degree of a Monomial

Polynomial

Degree of a Polynomial

An expression that is either a number, variable, or the produ…

The sum of the exponents of the variables

A sum of monomials

The greatest degree of the terms in a polynomial

Monomial

An expression that is either a number, variable, or the produ…

Degree of a Monomial

The sum of the exponents of the variables

Monomial

Polynomial

Term

Binomial

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

A monomial or a sum of monomials

Each monomial part of a polynomial

A polynomial with exactly 2 terms

Monomial

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

Polynomial

A monomial or a sum of monomials

constant

monomial

coefficient

degree of a variable in a monomial

any number

a constant, variable, or a product of a constant and one or m…

the constant factor in a monomial (coefficient of -st is 1)

the number of times a variable occurs as a factor in the mono…

constant

any number

monomial

a constant, variable, or a product of a constant and one or m…

factored form

equation

linear term

quadratic term

an expression written as a product of factors ... ex. x(x+2) is…

two expressions that are equal (=)

a term with degree 1... ex. -2x, 7a, 6d

a term with degree 2 ... ex. ab, y^2

factored form

an expression written as a product of factors ... ex. x(x+2) is…

equation

two expressions that are equal (=)

Polynomial

Term

Constant

Coefficient

A term or group of terms (cannot have a negative exponent or…

A constant (number), a variable, and a coefficient with a var…

A number without a variable

The number part of a term with a variable

Polynomial

A term or group of terms (cannot have a negative exponent or…

Term

A constant (number), a variable, and a coefficient with a var…

Long Division Tips

Long Division Rules

Synthetic Division Tips

Synthetic Divison Rules

- make sure everything is in ascending order ... - add 0() if a…

- take the first term of the dividend and divide it by the fi…

- make sure everything is in ascending order ... - put 0() if a…

- put all of the coefficients of the dividend together (make…

Long Division Tips

- make sure everything is in ascending order ... - add 0() if a…

Long Division Rules

- take the first term of the dividend and divide it by the fi…

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

Degree

Monomial

Binomial

Trinomial

For a monomial the degree is the sum of the exponents of the…

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

A polynomial with two terms.

A polynomial with three terms.

Degree

For a monomial the degree is the sum of the exponents of the…

Monomial

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

Binomial Theorem

Conjugate Root Theorem

degree of a monomial

degree of a polynomial

gives a general formula for expanding the binomial, (a + b)^n…

if P(a) is a polynomial with rational or real coefficients, t…

the exponent of the variable in the expression

the greatest degree among the monomial terms

Binomial Theorem

gives a general formula for expanding the binomial, (a + b)^n…

Conjugate Root Theorem

if P(a) is a polynomial with rational or real coefficients, t…

Polynomial

Difference of Squares

Factor

Trinomial

an expression with two or more terms

a^2 -b^2 = (a+b)(a-b)

Break a number into at least two numbers that are multiplied

A polynomial with three terms

Polynomial

an expression with two or more terms

Difference of Squares

a^2 -b^2 = (a+b)(a-b)

standard form

continuous; smooth

all real numbers

possible real

polynomials are ________ and _________ with no jumps, breaks,…

a polynomial's domain is...

p/q is used to find ______, ________ solutions

standard form

continuous; smooth

polynomials are ________ and _________ with no jumps, breaks,…

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

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

Degree of a Monomial

Polynomial

Binomial

one term that consists of a number, a variable, or the produc…

The sum of the exponents of the variables in the monomial

a monomial or the sum of monomials, each called a term. Terms…

a polynomial with 2 terms

Monomial

one term that consists of a number, a variable, or the produc…

Degree of a Monomial

The sum of the exponents of the variables in the monomial

Monomial

Degree of a Monomial

Polynomial

Binomial

one term that consists of a number, a variable, or the produc…

The sum of the exponents of the variables in the monomial

a monomial or the sum of monomials, each called a term. Terms…

a polynomial with 2 terms

Monomial

one term that consists of a number, a variable, or the produc…

Degree of a Monomial

The sum of the exponents of the variables in the monomial

Long Division with polynomials

Synthetic Division with polynomials

Summary of Synthetic Division

Remainder Theorem

- place the root on the side and the coefficients of the divi…

- Divisor must be linear... - divide using root k, not factor x-…

- How to calculate the remainer

Long Division with polynomials

Synthetic Division with polynomials

- place the root on the side and the coefficients of the divi…

degree (of a polynomial)

terms

polynomial in standard form

polynomial

the sum of the exponents of the variables contained in the term

a number, variable or the product of a number and /or variabl…

a polynomial whose terms are written in descending order of d…

a single term or or the sum of two or more terms

degree (of a polynomial)

the sum of the exponents of the variables contained in the term

terms

a number, variable or the product of a number and /or variabl…

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+…