#### Study sets matching "algebra factoring"

#### Study sets matching "algebra factoring"

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.

BEFORE STARTING PROBLEM

two terms

three terms

difference of squares

FIND GCF

- difference of squares... - sum of cubes... - difference of cubes

- perfect square trinomials... - (x ___) (x___)... -grouping

- both perfect squares... - Difference (-)... *A^2 - B^2 = (A-B) (A…

BEFORE STARTING PROBLEM

FIND GCF

two terms

- difference of squares... - sum of cubes... - difference of cubes

Binomial

Degree of a Monomial

Degree of a Polynomial

Difference of Two Squares

An expression that is the sum of two numbers. Example: 2x + 8

The sum of all the exponents in a single term ... Example: 4x^6;…

The greatest degree of any term in the polynomial. Example: -…

Two perfect squares separated by a subtraction sign. a^2 - b^…

Binomial

An expression that is the sum of two numbers. Example: 2x + 8

Degree of a Monomial

The sum of all the exponents in a single term ... Example: 4x^6;…

Difference of two perfect squares

Sum of two perfect squares

Trinomial squares

Generic trinomials ax^2+bx+c

A^2-B^2=(A+B)(A-B)

Doesn't factor

A^2+2AB+B^2=(A+B)^2... A^2-2AB+B^2=(A-B)^2

Guess and check

Difference of two perfect squares

A^2-B^2=(A+B)(A-B)

Sum of two perfect squares

Doesn't factor

Perfect square

Formula for factoring two different sq…

How can 2x(x^2-4) be simplified?

Trinomial Factoring

Coefficient is a perfect square number... Exponents are even num…

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

2x(x+2)(x-2)

Working backwards.

Perfect square

Coefficient is a perfect square number... Exponents are even num…

Formula for factoring two different sq…

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

Factor by Grouping

The number game

Advanced # game is same as

Substituion

Ab-6a+2b-12... A(b-6) 2(b-6)

X^2+10x+16... Mult:16... Add:10... 2,8... X^2+2x+8x+16... X(x+2)+8(x+2)... (X+8…

.# game expect mult first and last #

5x^4+29x^2-42... Let y=x^2... 5y^2+29y-42... Then advanced # game

Factor by Grouping

Ab-6a+2b-12... A(b-6) 2(b-6)

The number game

X^2+10x+16... Mult:16... Add:10... 2,8... X^2+2x+8x+16... X(x+2)+8(x+2)... (X+8…

Binomial

Degree of a Monomial

Degree of a Polynomial

Difference of Two Squares

An expression that is the sum of two numbers. Example: 2x + 8

The sum of all the exponents in a single term ... Example: 4x^6;…

The greatest degree of any term in the polynomial. Example: -…

Two perfect squares separated by a subtraction sign. a^2 - b^…

Binomial

An expression that is the sum of two numbers. Example: 2x + 8

Degree of a Monomial

The sum of all the exponents in a single term ... Example: 4x^6;…

factor

perfect square

Trinomial

Prime Number

A number or polynomial that divides evenly into a number or p…

The square of a rational number

A polynomial with 3 terms

A natural number greater than 1 that has no positive divisors…

factor

A number or polynomial that divides evenly into a number or p…

perfect square

The square of a rational number

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…

(x-6)(x+3) (tip: since a=1, use guess…

(x + 2)(x + 3) (tip: since a=1, use gu…

(x - 3)(x - 4) (tip: since a=1, use gu…

(x + 8)(x - 2) (tip: since a=1, use gu…

Factor x² - 3x - 18

Factor x² + 5x + 6

Factor x² -7x + 12

Factor x² + 6x -16

(x-6)(x+3) (tip: since a=1, use guess…

Factor x² - 3x - 18

(x + 2)(x + 3) (tip: since a=1, use gu…

Factor x² + 5x + 6

Factor by grouping

Factor each trinomial

Factor each trinomial (a>1)

Factor difference of squares

To be used with four-number equations (ex: 8x^3-4x^2+28x-14).…

To be used with three-number equations (Ex: x^2-11x+10) Find…

To be used with three-numver equations where the first number…

To be used with two-number equations. Find the square root of…

Factor by grouping

To be used with four-number equations (ex: 8x^3-4x^2+28x-14).…

Factor each trinomial

To be used with three-number equations (Ex: x^2-11x+10) Find…

Prime Number

Greatest Common Factor

Factor (verb)

Common Factor

An integer greater than 1 that has no positive integral facto…

The common factor with the greatest coefficient and the great…

Write a number as a product of numbers in a set.

A factor of two or more integers.

Prime Number

An integer greater than 1 that has no positive integral facto…

Greatest Common Factor

The common factor with the greatest coefficient and the great…

8x²y²(9x⁵ - 2y)... [just GCF]

-9y⁹(1 + 2x²)... [just GCF]

4a³b(5ab⁴ + 2a² - 1)... [just GCF]

x(x³ + 3x - 7) ... [just GCF]

Factor Completely... 72x⁷y² - 16x²y³

Factor Completely... -9y⁹ - 18y⁹x²

Factor Completely... 20a⁴b⁵ + 8a⁵b - 4a³b

Factor Completely... x⁴ + 3x² - 7x

8x²y²(9x⁵ - 2y)... [just GCF]

Factor Completely... 72x⁷y² - 16x²y³

-9y⁹(1 + 2x²)... [just GCF]

Factor Completely... -9y⁹ - 18y⁹x²

First step in factoring

Difference of 2 squares (binomial)

Difference of 2 cubes (binomial)

Sum of 2 cubes (binomial)

FIND GCF

a(squared) - b(squared) = (a-b)(a+b)

a(cubed) - b(cubed) = [(a-b)(a(squared)) + ab + b(squared)]

a(cubed) + b(cubed) = [(a+b)(a(squared))-ab+b(squared)]

First step in factoring

FIND GCF

Difference of 2 squares (binomial)

a(squared) - b(squared) = (a-b)(a+b)

prime number

composite number

prime factorization

factored form

A whole number greater than 1 that has exactly two factors, i…

A whole number greater than 1 that has more than 2 factors.

A whole number expressed as a product of factors that are all…

A monomial expressed as a product of prime numbers and variab…

prime number

A whole number greater than 1 that has exactly two factors, i…

composite number

A whole number greater than 1 that has more than 2 factors.

Polynomial

Greatest Common Factor (GCF)

Degree

Term

A monomial or the sum of monomials.

The common factor with the greatest coefficient and the great…

The exponent of the variable in a term.

A number, a variable, or the product of a number and one or m…

Polynomial

A monomial or the sum of monomials.

Greatest Common Factor (GCF)

The common factor with the greatest coefficient and the great…

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

8x²y²(9x⁵ - 2y)... [just GCF]

-9y⁹(1 + 2x²)... [just GCF]

4a³b(5ab⁴ + 2a² - 1)... [just GCF]

x(x³ + 3x - 7) ... [just GCF]

Factor Completely... 72x⁷y² - 16x²y³

Factor Completely... -9y⁹ - 18y⁹x²

Factor Completely... 20a⁴b⁵ + 8a⁵b - 4a³b

Factor Completely... x⁴ + 3x² - 7x

8x²y²(9x⁵ - 2y)... [just GCF]

Factor Completely... 72x⁷y² - 16x²y³

-9y⁹(1 + 2x²)... [just GCF]

Factor Completely... -9y⁹ - 18y⁹x²

quadratic expression

quadratic equation

factor

monomial

a polynomial expression with degree 2 (ax^2+bx+c)

a second-degree polynomial equation in a single variable with…

break up a number into the product of smaller numbers.

a polynomial expression with one term.

quadratic expression

a polynomial expression with degree 2 (ax^2+bx+c)

quadratic equation

a second-degree polynomial equation in a single variable with…

monomial

degree of a monomial

polynomial

degree of a polynomial

an expression with one term

the sum of the exponents WITH A VARIABLE

a monomial with one or more terms

the degree of the largest exponent

monomial

an expression with one term

degree of a monomial

the sum of the exponents WITH A VARIABLE

composite number

factored form

factoring

factoring by grouping

A whole number, greater than one, that has more than two fact…

A monomial expressed as a product of prime numbers and variab…

To express a polynomial as the product of monomials and polyn…

The use of the distributive property to factor some polynomia…

composite number

A whole number, greater than one, that has more than two fact…

factored form

A monomial expressed as a product of prime numbers and variab…

The degree of the polynomial tells you…

positive leading coefficient to an eve…

positive leading coefficient to an odd…

negative leading coefficient to an eve…

-end behavior... odd degree: the ends go in different directions…

- as x reaches positive infinity f(x) reaches positive infini…

- as x reaches positive infinity f(x) reaches positive infini…

- as x reaches positive infinity f(x) reaches negative infini…

The degree of the polynomial tells you…

-end behavior... odd degree: the ends go in different directions…

positive leading coefficient to an eve…

- as x reaches positive infinity f(x) reaches positive infini…

Factoring

Greatest Common Factor

Monomials

Binomials

The process of expressing a given number or expression as a p…

The greatest factor that divides two numbers.

A number or a variable or the product of numbers and or a var…

A polynomial with two terms.

Factoring

The process of expressing a given number or expression as a p…

Greatest Common Factor

The greatest factor that divides two numbers.

The biggest number that divides evenly…

Numbers that don't share any common fa…

1- GCF... 2- Trinomial into two binomials…

The product.

What is the greatest common factor?

What does relatively prime mean?

What are the steps to a factor flow chart?

What is the third term of a trinomial? ( the 15 in x^2 + 8x +…

The biggest number that divides evenly…

What is the greatest common factor?

Numbers that don't share any common fa…

What does relatively prime mean?

8x²y²(9x⁵ - 2y)... [just GCF]

-9y⁹(1 + 2x²)... [just GCF]

4a³b(5ab⁴ + 2a² - 1)... [just GCF]

x(x³ + 3x - 7) ... [just GCF]

Factor Completely... 72x⁷y² - 16x²y³

Factor Completely... -9y⁹ - 18y⁹x²

Factor Completely... 20a⁴b⁵ + 8a⁵b - 4a³b

Factor Completely... x⁴ + 3x² - 7x

8x²y²(9x⁵ - 2y)... [just GCF]

Factor Completely... 72x⁷y² - 16x²y³

-9y⁹(1 + 2x²)... [just GCF]

Factor Completely... -9y⁹ - 18y⁹x²

(x-6)(x+3) (tip: since a=1, use guess…

(x + 2)(x + 3) (tip: since a=1, use gu…

(x - 3)(x - 4) (tip: since a=1, use gu…

(x + 8)(x - 2) (tip: since a=1, use gu…

Factor x² - 3x - 18

Factor x² + 5x + 6

Factor x² -7x + 12

Factor x² + 6x -16

(x-6)(x+3) (tip: since a=1, use guess…

Factor x² - 3x - 18

(x + 2)(x + 3) (tip: since a=1, use gu…

Factor x² + 5x + 6

factor completly

factory by grouping

solving equations

trial and error

- find GCF ... -NO =0 ... - NO x=#... * 2k^2+6k-20 ... 2(k+3k-10) ... 2(k+5…

- pairs... - find GCF of both pairs of numbers ... - then multiply…

- factor ... - no GCF ... - YES =0 ... - YES x=#... * x^2-2x-15=0 ... (x-5…

- outside numbers and inside number ... * 2x^2+3x-2=0... (2x-1)(3…

factor completly

- find GCF ... -NO =0 ... - NO x=#... * 2k^2+6k-20 ... 2(k+3k-10) ... 2(k+5…

factory by grouping

- pairs... - find GCF of both pairs of numbers ... - then multiply…