Grade 9: Algebra Flashcards

Questions and Answers

What is the definition of Algebra?

Individual parts of an expression

A combination of numbers symbols and variables with an equal sign

The number that divides exactly into another number

Letters and symbols are used to represent numbers and their relationships (correct)

What is an Expression?

A combination of numbers symbols and variables that has no equal sign.

What are Coefficients?

The number before the variable.

What is a Variable?

The unknown term that can have exponents. Signup and view all the answers

What is a Constant?

A number with no variable attached. Signup and view all the answers

What is a Term in mathematics?

Individual parts of an expression. Signup and view all the answers

What is the Degree of a term?

The sum of all exponents on all variables in the term. Signup and view all the answers

What is a Polynomial?

Algebraic expressions that are made of terms and are all connected by addition and subtraction. Signup and view all the answers

What is a Monomial?

An expression that has 1 term. Signup and view all the answers

What is a Binomial?

An expression that has 2 terms. Signup and view all the answers

What is a Trinomial?

An expression that has 3 terms. Signup and view all the answers

What is the Degree of a Polynomial?

The term with the highest degree of term within the polynomial. Signup and view all the answers

What is a Factor?

A number that divides exactly into another number. Signup and view all the answers

What is Factoring?

Finding what to multiply together. Signup and view all the answers

What is a Common Factor?

The factor out the GCF in an expression. Signup and view all the answers

How do you identify the degree of a term?

By summing all exponents on all variables in the term. Signup and view all the answers

How do you collect like terms?

Group terms with the same variables (including exponents) together. Signup and view all the answers

How do you multiply monomials?

You multiply the coefficients and add the exponents. Signup and view all the answers

How do you divide monomials?

Divide the coefficients and subtract the exponents. Signup and view all the answers

How do you apply power of a power rules to monomials?

Multiply the exponents together. Signup and view all the answers

How do you add and subtract polynomials?

By collecting like terms. Signup and view all the answers

How do you multiply polynomials?

Use the distributive property or FOIL method. Signup and view all the answers

How do you divide polynomials?

Use polynomial long division or synthetic division. Signup and view all the answers

How do you expand binomials?

Use the distributive property or special multiplication rules. Signup and view all the answers

How do you common factor?

Identify the greatest common factor and factor it out from each term. Signup and view all the answers

Study Notes

Algebra Basics

Algebra involves using letters and symbols to represent numbers and express their relationships.
An expression combines numbers, symbols, and variables, but does not have an equal sign.

Key Terms

Coefficients: The numerical part placed before a variable in an algebraic term.
Variables: The unknown elements in an expression that can have exponents.
Constants: Numbers that do not change and are not accompanied by variables.
Terms: The distinct components that make up an expression, either variables, constants, or products.

Terms and Degrees

Degree of a Term: Calculated by summing the exponents of all variables within that term.
Polynomial: An expression containing multiple terms connected by addition or subtraction.
Types of polynomials include:
- Monomial: Contains one term.
- Binomial: Contains two terms.
- Trinomial: Contains three terms.
Degree of Polynomial: The term with the highest degree within the polynomial dictates the overall degree.

Factoring and Common Factors

Factor: A number that divides another number without leaving a remainder.
Factoring: The process of identifying multiple components that can be multiplied to yield a particular expression.
Common Factor: The largest factor shared among terms in an expression, often determined by the Greatest Common Factor (GCF).

Operations with Terms and Polynomials

Identifying degrees:
- Utilize alphabetical ordering to identify the degree of terms, for instance, in 7xy, the degree is 2.
Collecting Like Terms: Group terms that share the same variables and exponents to simplify expressions.
Multiplying Monomials: Multiply coefficients and add exponents for like variables.
Dividing Monomials: Divide coefficients and subtract exponents for like variables.

Power Rules and Polynomials

Applying the power of a power rule involves raising each component to the appropriate exponent, e.g., ((4c^3d^4)^2 = 16c^6d^8).

Adding and Subtracting Polynomials

Combine like terms by aligning similar variables and coefficients, e.g., simplifying ((3a - 2b + c - 10) + (6a + c - 4) - (14b - 3c)) results in (9a - 16b + 5c - 14).

Multiplying and Dividing Polynomials

Multiplying Polynomials: Use the distributive property (rainbow method) to expand polynomials such as (3x(4x^2y + 2xy - 7) + 2x^3(3x - 5xy + 2)).
Dividing Polynomials: Similar to monomial division but considers polynomial structure.

Expanding and Common Factoring

Expanding Binomials: The double rainbow method expands products such as (-5(2x - 1)(5x^2 - 3x - 2)) into a polynomial expression.
Common Factoring: Reverse expand by factoring out the GCF from an expression to simplify further, e.g., (9x^2y^3 + 12xy^4 - 18x^3y^2 + 3xy^2) becomes (3xy^2(3xy + 4y^2 - 6x^2 + 1)).

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Test your knowledge with these Algebra flashcards designed for 9th-grade students. Each card features key terms and definitions that are essential for mastering algebra concepts. Perfect for quick reviews and memorization.