# Study sets matching "algebra factoring"

Study sets

Diagrams

Classes

Users

Monomial

degree of a monomial

Polynomial

Standard form of a polynomial

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

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 o…

Monomial

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

degree of a monomial

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

Monomial

degree of a monomial

Polynomial

Standard form of a polynomial

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

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 o…

Monomial

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

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

Polynomial

Greatest Common Factor (GCF)

Degree

Term

A monomial or the sum of monomials. (many numbers)

The common factor with the greatest coefficient and the greate…

The exponent of the variable in a term.

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

Polynomial

A monomial or the sum of monomials. (many numbers)

Greatest Common Factor (GCF)

The common factor with the greatest coefficient and the greate…

Polynomial

Monomial

Binomial

Trinomial

A term or the sum or difference of terms

An expression with one term; a number, a variable, or the prod…

A polynomial with two terms

A polynomial with three terms

Polynomial

A term or the sum or difference of terms

Monomial

An expression with one term; a number, a variable, or the prod…

What are the general steps in when fact…

How do you factor a quadratic such as t…

How do you factor a difference of two s…

How do you factor a difference OR sum o…

1. Find the GCF: the biggest factor that you can pull out of e…

(a +- b)(a+-b) ... (a plus or minus b) times (a plus or minus b)…

(a + b)(a-b) where: ... a = square root of first term ... b = squar…

DIFFERENCE OF TWO CUBES... (a-b)(a^2+ab+b^2) where... a=cube root…

What are the general steps in when fact…

1. Find the GCF: the biggest factor that you can pull out of e…

How do you factor a quadratic such as t…

(a +- b)(a+-b) ... (a plus or minus b) times (a plus or minus b)…

Factor by Grouping

AC-Method for Factoring Trinomials

Prime Polynomial

Difference of Squares

b^2 - 2b +yb -2y factors as b(b-2) + y(b - 2), then factor out…

Factor out the GCF from all terms. Find the product ac. Find t…

A polynomial whose only factors are 1 and itself.

a^2 - b^2 factors as (a - b)(a + b)... Ex. 4x^2 - 25... (4x - 5)(4x…

Factor by Grouping

b^2 - 2b +yb -2y factors as b(b-2) + y(b - 2), then factor out…

AC-Method for Factoring Trinomials

Factor out the GCF from all terms. Find the product ac. Find t…

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: -7…

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

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;…

binomial

degree of a monomial

degree of a polynomial

difference of two squares

A polynomial with two terms

The sum of the exponents of the variables of a monomial

The greatest degree of any term in the polynomial

a² - b² = (a + b)(a - b)

binomial

A polynomial with two terms

degree of a monomial

The sum of the exponents of the variables of a 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

monomial

degree

polynomial

leading coefficient

an algebraic expression consisting of one term.

highest exponent in polynomial, trinomial, and binomial

an expression of more than two algebraic terms, especially the…

the numbers are written in front of the variable with the larg…

monomial

an algebraic expression consisting of one term.

degree

highest exponent in polynomial, trinomial, and binomial

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 squ…

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

Trinomial Factoring

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

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 numb…

Formula for factoring two different squ…

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

What are the two methods to find the pr…

Find the prime factorization of 40

Find the prime factorization of 17

What are the two methods to find the GC…

1. Factor tree... 2. Ladder diagram

40... 10 * 4... 5 * 2 * 2 * 2... 2³ * 5

17... 17 * 1 or just 17

1. List the factors... 2. Prime Factorization

What are the two methods to find the pr…

1. Factor tree... 2. Ladder diagram

Find the prime factorization of 40

40... 10 * 4... 5 * 2 * 2 * 2... 2³ * 5