Polynomials and Algebraic Expressions (9th grade FT)

Questions and Answers

What is a polynomial?

An expression with no variables

A single algebraic term

An expression of exactly two algebraic terms

An expression of more than two algebraic terms (correct)

What is a monomial?

A number, a variable, or a product of a number and one or more variables.

What is a binomial?

A polynomial with two terms.

What is a trinomial?

A polynomial with three terms. Signup and view all the answers

Define an algebraic expression.

A combination of variables, numbers, and at least one operation. Signup and view all the answers

What are like terms?

Terms that contain the same variables raised to the same power. Signup and view all the answers

What is a perfect square?

A number that is the square of an integer. Signup and view all the answers

What is an equation?

A mathematical statement that two expressions are equal. Signup and view all the answers

What is a leading coefficient?

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

What is standard form of a polynomial?

A polynomial that is written with the terms in order from greatest degree to least degree. Signup and view all the answers

Define a variable in mathematics.

A symbol used to represent a quantity that can change. Signup and view all the answers

What is an expression?

A mathematical phrase that contains operations, numbers, and/or variables. Signup and view all the answers

What are inverse operations?

Operations that undo each other. Signup and view all the answers

What does equivalent mean in mathematics?

Equal. Signup and view all the answers

What is a coefficient?

A number in front of a variable. Signup and view all the answers

Define terms in algebra.

A number, a variable, or a product of numbers and variables. Signup and view all the answers

What is a constant term?

A term without a variable. Signup and view all the answers

What does combining like terms mean?

To simplify an expression, combine common variable terms and constant terms. Signup and view all the answers

What is the Distributive Property?

A property that states a(b + c) = ab + ac or a(b - c) = ab - ac. Signup and view all the answers

What is the simplest form of an algebraic expression?

An algebraic expression is in simplest form when it has no like terms and no parentheses. Signup and view all the answers

What does factoring mean?

Rewriting an expression as the product of its factors. Signup and view all the answers

Define the greatest common factor (GCF).

The largest factor that two or more numbers have in common. Signup and view all the answers

What is a variable term?

A term that contains a variable. Signup and view all the answers

Study Notes

Polynomials and Algebraic Expressions

Polynomials: Consist of more than two algebraic terms.
Monomial: Can be a single number, a variable, or a combination of both.
Binomial: Defined as a polynomial formed from exactly two terms.
Trinomial: A polynomial containing three distinct terms.

Algebraic Concepts

Algebraic Expression: Made up of numbers, variables, and at least one operation like addition or multiplication.
Like Terms: Terms that share identical variable factors raised to the same power, allowing them to be combined.
Perfect Square: A number that results from squaring an integer.

Mathematical Statements

Equation: Represents a mathematical assertion that two expressions hold equal value.
Leading Coefficient: Identifies the coefficient in the term with the highest degree in a polynomial.

Polynomial Characteristics

Standard Form: Polynomials organized in descending order by degree.
Variable: A symbol that signifies a changing quantity.
Expression: Refers to a mathematical statement that includes numbers, operations, and/or variables.

Properties and Operations

Inverse Operations: Refer to operations that cancel each other out (e.g., addition and subtraction).
Equivalent: Terms or expressions that hold equal value.
Coefficient: The numerical factor that precedes a variable in an expression.

Structural Elements of Expressions

Terms: Can be standalone numbers, variables, or a mix of both.
Constant Term: A specific term devoid of a variable component.
Combining Like Terms: The process of simplifying expressions by merging terms with the same variables and constants.

Algebraic Techniques

Distributive Property: A critical algebraic principle stating a(b + c) = ab + ac, used for expanding expressions.
Simplest Form: A state where an algebraic expression has no like terms and no parentheses remaining.
Factoring: The method of rewriting an expression as a product of its factors.

Factors in Mathematics

Greatest Common Factor (GCF): The largest factor shared by two or more numbers.
Variable Term: Specifically refers to any term in an expression that includes a variable.

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Description

Test your knowledge of polynomials and algebraic expressions with this quiz. Learn the definitions of key terms such as monomials, binomials, and trinomials. Perfect for 9th grade students preparing for algebra assessments.