Algebra II Module 3 Flashcards

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Questions and Answers

What is an expression?

A term with a coefficient and two variables.
A combination of constants and variables that is equal to something.
Any combination of constants, variables, or coefficients that is not set equal to anything. (correct)
An equation that represents a polynomial.

What is a term?

A term is any constant, variable, or coefficient and its variable(s), separated by addition or subtraction signs.

How are polynomials typically arranged?

A polynomial's terms are arranged in descending order based on each term's exponent.

What is the degree of a polynomial?

The degree is the greatest degree of any term in the polynomial. Signup and view all the answers

What is a monomial?

An equation or expression with only one term. Signup and view all the answers

What is a binomial?

An equation or expression with two terms. Signup and view all the answers

What is a trinomial?

An equation or expression with three terms. Signup and view all the answers

What is a polynomial?

An equation or expression with four or more terms. Signup and view all the answers

What are the steps for adding polynomials?

Step 1: Distribute any coefficients. Step 2: Combine like terms. Signup and view all the answers

How do you subtract polynomials?

It is similar to adding polynomials, but distribute a negative one. Signup and view all the answers

What does the Distributive Property state?

When multiplying a factor and a quantity in parentheses, multiply the factor to each term inside. Signup and view all the answers

What does FOIL stand for?

First Terms, Outside Terms, Inside Terms, Last Terms. Signup and view all the answers

What is the Greatest Common Factor (GCF)?

The GCF is the largest factor that all terms in a polynomial have in common. Signup and view all the answers

What is a difference of squares?

A binomial where both terms are perfect squares, subtracted. Signup and view all the answers

What pattern does a perfect square trinomial follow?

It can be factored using $a^2 + 2ab + b^2 = (a + b)^2$ or $a^2 - 2ab + b^2 = (a - b)^2$. Signup and view all the answers

What are the steps for factoring trinomials?

Step 1: Factor for GCF. Step 2: Determine the binomial factors. Step 3: Check the factors using FOIL. Signup and view all the answers

What does factoring by grouping involve?

Step 1: Factor out GCF. Step 2: Group terms. Step 3: Factor the GCF from each group. Step 4: Factor the common binomial. Signup and view all the answers

What is a perfect cube?

A three-dimensional object whose volume is found by multiplying the length, width, and height, which are all equal. Signup and view all the answers

What is the formula for the difference of cubes?

The formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Signup and view all the answers

What is the formula for the sum of cubes?

The formula is $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Signup and view all the answers

What are the steps for expanding binomials using Pascal's Triangle?

Step 1: Identify the coefficients. Step 2: Substitute the second component. Step 3: Substitute the third component. Signup and view all the answers

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Study Notes

Algebra II Module 3 Concepts

Expression: A combination of constants, variables, or coefficients without an equality sign.
Term: The basic building block comprising a constant, variable, or coefficients paired with variables, separated by addition or subtraction.
Polynomial Arrangement: Terms arranged in descending order based on the exponent of each term.
Degree of Polynomials: The highest exponent value in a polynomial; e.g., ( g^4 - 16g^3 ) has a degree of 4, whereas ( x^3y^2 + 9x^2y ) has a degree of 5 (3 + 2).
Monomial: An expression consisting of a single term, such as ( 3p ).
Binomial: An expression with exactly two terms, for instance, ( 3p + 2x^2 ).
Trinomial: An expression that has three terms, like ( 3p + 2x^2 - 2xy ).
Polynomial: An expression with four or more terms, such as ( 3p + 2x^2 - 2xy - 5x^2 ).
Adding Polynomials: Requires distributing any coefficients and combining "like terms" with identical exponents.
Subtracting Polynomials: Similar to addition, but includes distributing a negative sign across the polynomial being subtracted.
Distributive Property: When multiplying, distribute the factor to each term inside parentheses, including exponents.
Multiplying Binomials (FOIL): Use the First, Outside, Inside, and Last method for multiplying binomials.
Greatest Common Factors (GCF): The largest factor shared by all terms, useful for simplifying expressions.
Difference of Squares Binomial: A binomial ( a^2 - b^2 ) that factors into ( (a + b)(a - b) ).
Perfect Square Trinomial: A trinomial ( a^2 + 2ab + b^2 ) that factors into ( (a + b)^2 ) or ( a^2 - 2ab + b^2 ) that factors into ( (a - b)^2 ).
Factoring Trinomials: Involves factoring out the GCF, determining binomial factors, and verifying results via FOIL.
Factoring by Grouping (Four-Term Polynomials): Factor out the GCF, group terms, factor the GCF from groups, factor the common binomial, and check via FOIL.
Perfect Cube: A three-dimensional shape with equal length, width, and height, where volume equals the cube of one dimension.
Difference of Cubes: The polynomial ( a^3 - b^3 ) can be factored as ( (a - b)(a^2 + ab + b^2) ).
Sum of Cubes: The polynomial ( a^3 + b^3 ) can be factored as ( (a + b)(a^2 - ab + b^2) ).
Expanding Binomials (Pascal's Triangle): Identify coefficients and substitute components step-by-step to expand binomials correctly.