#### Study sets matching "polynomials chapter 5"

#### Study sets matching "polynomials chapter 5"

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…

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

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)

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…

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…

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…

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 the Monomial

Rule For Multiplying Exponential Expre…

Rule For Dividing Exponential Expressi…

a number, a variable, or a product of a number and variables.

sum of the exponents of the variables

If same base and multiplying= add exponents

If same base and dividing= subtract the exponents

monomial

a number, a variable, or a product of a number and variables.

Degree of the Monomial

sum of the exponents of the variables

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

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…

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…

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 coeffients (not bases) and add exponents... x^m+n

multiply exponents, if there is a coefficient, multiply that…

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

subtract the exponents... x^m-n

when multiplying two numbers with expo…

multiply coeffients (not bases) and add exponents... x^m+n

when a number with an exponent has an…

multiply exponents, if there is a coefficient, multiply that…

degree of a polynomial

depressed polynomial

end behavior

extrema

The degree of the monomial with the greatest degree

A polynomial that has a degree one less than the original pol…

The behavior of the graph of f(x) as x approaches positive in…

The maximum and minimum values of a polynomial function

degree of a polynomial

The degree of the monomial with the greatest degree

depressed polynomial

A polynomial that has a degree one less than the original pol…

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

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

Polynomial

Degree

Multiplying two binomials

Linear

An expression that has no operations other than addition, sub…

The highest power of a variable that appears in a polynomial…

1. Multiply each term of one term by the other. 2. Combine li…

A word describing a first degree polynomial

Polynomial

An expression that has no operations other than addition, sub…

Degree

The highest power of a variable that appears in a polynomial…

Remainder theorem

Factor theorem

Fundamental Theorem of Algebra

Conjugate root theorem

A theorem that states: for a polynomial P(x), the value P(c)…

A remainder theorem that states that the polynomial p(x) has…

A theorem that says every polynomial function with a degree o…

A theorem that says if a + bi is root of a polynomial with re…

Remainder theorem

A theorem that states: for a polynomial P(x), the value P(c)…

Factor theorem

A remainder theorem that states that the polynomial p(x) has…

binomial

highest

coefficient

trinomial

A polynomial containing two terms is called a ________.

The degree of a polynomial is the degree of its ___________ d…

The numerical factor in a monomial is called the __________.

A polynomial containing three terms is called a __________.

binomial

A polynomial containing two terms is called a ________.

highest

The degree of a polynomial is the degree of its ___________ d…

Monomial

Binomial

Trinomial

Polynomial

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

Two monomials added or subtracted

Three monomials added or subtracted

Four or more monomials added or subtracted

Monomial

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

Binomial

Two monomials added or subtracted

Monomial

Degree of a monomial

Polynomial

Degree of a polynomial

A number, a variable, or a product of numbers and variables w…

The sum of the exponents of the variables.

A monomial or a sum or difference of monomials.

The degree of the term with the greatest degree.

Monomial

A number, a variable, or a product of numbers and variables w…

Degree of a monomial

The sum of the exponents of the variables.

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…

Multiplying Monomials

Multiplying Monomials With More Than O…

Multiplying a Monomial by a Polynomial

Multiplying Two Polynomials

First we multiply the coefficients, and then we multiply the…

First we multiply the coefficients, and then we multiply the…

We multiply the monomial by each term of the polynomial.... To d…

To multiply Polynomials containing more than two terms, we mu…

Multiplying Monomials

First we multiply the coefficients, and then we multiply the…

Multiplying Monomials With More Than O…

First we multiply the coefficients, and then we multiply the…

900x³ - 4x

x⁴ - 10x³ + 25x²

6x² + 17x + 5

8x² - 14x + 3

Multiply... x(30x - 2)(30x + 2)

Multiply... x²(x - 5)(x + 5)

Multiply... (3x + 1)(2x + 5)

Multiply... (1 - 4x)(3 - 2x)

900x³ - 4x

Multiply... x(30x - 2)(30x + 2)

x⁴ - 10x³ + 25x²

Multiply... x²(x - 5)(x + 5)

Polynomial

Standard Form of a Polynomial

Coefficient

Monomial

A monomial or a sum or difference of monomials.

Arrangement of terms in a polynomial where the highest degree…

A number that is multiplied by a variable.

A number or a product of numbers and variables with whole-num…

Polynomial

A monomial or a sum or difference of monomials.

Standard Form of a Polynomial

Arrangement of terms in a polynomial where the highest degree…

Polynomial

Standard Form of a Polynomial

Coefficient

Monomial

A monomial or a sum or difference of monomials.

Arrangement of terms in a polynomial where the highest degree…

A number that is multiplied by a variable.

A number or a product of numbers and variables with whole-num…

Polynomial

A monomial or a sum or difference of monomials.

Standard Form of a Polynomial

Arrangement of terms in a polynomial where the highest degree…

Polynomial function

Degree

Leading term

Leading coefficient

A function with any number of terms where each term is in the…

Value of a term's exponent

Term with highest degree

Largest number in front of a variable

Polynomial function

A function with any number of terms where each term is in the…

Degree

Value of a term's exponent

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+…

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

binomial

degree of a monomial

degree of a polynomial

difference of two squares

a polynomial consisting of two terms or monomials.

is the sum of exponents of its variables.

is the same as the degree of the monomial with the greatest d…

The difference pf two perfect square monomials.

binomial

a polynomial consisting of two terms or monomials.

degree of a monomial

is the sum of exponents of its variables.

Scientific Notation

polynomial

polynomial functions

leading coefficient

A number expressed in the form m × 10n

is a monomial or a sum of monomials

a polynomial is the sum of one or more monomials with real co…

The coefficient of the term with the highest degree

Scientific Notation

A number expressed in the form m × 10n

polynomial

is a monomial or a sum of monomials

monomials

polynomials

binomial

trinomial

a number, variable, or a product of numbers and variables wit…

monomial or sum of monomials

polynomial with two terms

polynomial with three terms

monomials

a number, variable, or a product of numbers and variables wit…

polynomials

monomial or sum of monomials

monomial

polynomial

degree of a monomial

degree of a polynomial

a number or a product of numbers and variables with whole num…

a monomial or a sum or difference of monomials

the sum of the exponents of the variables

given by the term with the greatest degree

monomial

a number or a product of numbers and variables with whole num…

polynomial

a monomial or a sum or difference of monomials

monomial

polynomial

degree of a monomial

degree of a polynomial

a number or a product of numbers and variables with whole num…

a monomial or a sum or difference of monomials

the sum of the exponents of the variables

given by the term with the greatest degree

monomial

a number or a product of numbers and variables with whole num…

polynomial

a monomial or a sum or difference of monomials

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…