Questions and Answers
What is an expression?
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?
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What is a monomial?
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What is a binomial?
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What is a trinomial?
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What is a polynomial?
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What are the steps for adding polynomials?
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How do you subtract polynomials?
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What does the Distributive Property state?
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What does FOIL stand for?
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What is the Greatest Common Factor (GCF)?
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What is a difference of squares?
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What pattern does a perfect square trinomial follow?
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What are the steps for factoring trinomials?
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What does factoring by grouping involve?
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What is a perfect cube?
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What is the formula for the difference of cubes?
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What is the formula for the sum of cubes?
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What are the steps for expanding binomials using Pascal's Triangle?
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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.
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Test your knowledge with these flashcards covering key concepts in Algebra II Module 3. Learn definitions and examples for essential terms such as expressions, terms, and polynomial arrangements. Perfect for revision or quick reference!