# Study sets matching "algebra factoring polynomial"

Study sets

Diagrams

Classes

Users

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…

degree of a monomial

standard form of a polynomial

monomial

binomial

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

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

A number, a variable, or a product of a number and one or more…

A polynomial with two terms.

degree of a monomial

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

standard form of a polynomial

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

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.

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…

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

to factor a number over a given set

prime number

prime factorization of a positive integ…

common factor of two integers

write the number as a product of numbers in that set

an integer greater than 1 that has no positive integer factors…

the integer is expressed as a product of primes

an integer that is a factor of both integers

to factor a number over a given set

write the number as a product of numbers in that set

prime number

an integer greater than 1 that has no positive integer factors…

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

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

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

Factor out the GCF

Examples of factoring out the GCF

Quadratic Trinomial

Examples of Quadratic Trinomial

Factoring out the greatest common factor of all terms

15x^4-20x^3+3x^2= 5x^2(3x^2-4x+7)

For ax^2+bx+c, find factors with product ac and sum b

6x^2+11x-10= (3x-2) (2x+5)

Factor out the GCF

Factoring out the greatest common factor of all terms

Examples of factoring out the GCF

15x^4-20x^3+3x^2= 5x^2(3x^2-4x+7)

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 de…

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.

Polynomial Function

Degree

Standard Form of a Polynomial

Relative Maximum

A function that can be written in the form f(x)= ax^n+ax^n-1+.…

The highest power, n. Is also the largest exponent of the func…

When all like terms have been combined, and the terms are writ…

A function value f(a) is called __________ of f if there is an…

Polynomial Function

A function that can be written in the form f(x)= ax^n+ax^n-1+.…

Degree

The highest power, n. Is also the largest exponent of the func…

a² - b²

a² + b²

a³ - b³

a³ + b³

(a-b)(a+b) [difference of squares]

sum of squares (can't be factored; prime)

(a-b)(a² + ab + b²) [difference of cubes]

(a+b)(a² - ab +b²) [sum of cubes]

a² - b²

(a-b)(a+b) [difference of squares]

a² + b²

sum of squares (can't be factored; prime)

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…

factoring form x^2+bx+c

factoring form ax^2+bx+c

a^2-b^2 (difference of two squares)

perfect square trinomial in form a^2+2a…

terms must add to bx and multiply to c

first and last terms multiplied + second and third terms multi…

(a+b)(a-b)

(a+b)^2

factoring form x^2+bx+c

terms must add to bx and multiply to c

factoring form ax^2+bx+c

first and last terms multiplied + second and third terms multi…

Scientific Notation

Polynomial

Polynomial Function

End Behavior

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

A monomial or sum of monomials.

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

Scientific Notation

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

Polynomial

A monomial or sum of monomials.