Polynomial Standard Form Flashcards

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Questions and Answers

What is Standard Form?

When the terms are arranged from the smallest exponent to the largest.

The highest degree present in the polynomial.

When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order. (correct)

A polynomial with exactly two terms.

What is a Term in a polynomial?

Each monomial in a polynomial.

Define Monomials.

A number, a variable, or the product of a number and one or more variables (no + or - present).

What is a Binomial?

A polynomial with exactly two terms. Signup and view all the answers

What is a Trinomial?

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

What is a polynomial with 4 terms called?

A polynomial with exactly four terms. Signup and view all the answers

What is the Degree of a polynomial?

The highest of the degrees of all its terms. Signup and view all the answers

What is a Constant?

A constant has no variable; it is just a number. Signup and view all the answers

What does Linear mean in polynomial terms?

The highest degree present in the polynomial is ONE; it is also called First Degree Polynomial. Signup and view all the answers

What does Quadratic mean in polynomial terms?

The highest degree present in the polynomial is TWO; it is also called Second Degree Polynomial. Signup and view all the answers

What does Cubic mean in polynomial terms?

The highest degree present in the polynomial is THREE; it is also called Third Degree Polynomial. Signup and view all the answers

What is a Coefficient?

A numerical factor in a term of an algebraic expression. Signup and view all the answers

What is a Leading Coefficient?

The coefficient of the first term in a polynomial written in standard form. Signup and view all the answers

What is a Constant Term?

A constant has no variable. Signup and view all the answers

What is a Linear Term?

The term containing x. Signup and view all the answers

What is the Coefficient of a Linear Term?

The numerical factor in a linear term. Signup and view all the answers

What is a Quadratic Term?

The term containing x^2. Signup and view all the answers

What is the Coefficient of a Quadratic Term?

The numerical factor in a quadratic term. Signup and view all the answers

Study Notes

Polynomial Standard Form

Standard form arranges polynomial terms from the highest to the lowest exponent in decreasing order.

Key Definitions

A term is defined as each individual monomial within a polynomial.
Monomials consist of a number, a variable, or the product of both, without any addition or subtraction present.
A binomial is characterized by having exactly two terms, while a trinomial contains exactly three terms.
Polynomials can also include four terms, referred to as a polynomial with four terms.

Polynomial Characteristics

The degree of a polynomial is determined by the highest degree of all its terms.
A constant is defined as a polynomial that does not contain any variables—only a number.

Types of Polynomials

Linear polynomials have a highest degree of one and are called first-degree polynomials.
Quadratic polynomials have a highest degree of two and are often referred to as second-degree polynomials.
Cubic polynomials possess a highest degree of three, referred to as third-degree polynomials.

Polynomial Components

A coefficient is the numerical factor found in a term of an algebraic expression.
The leading coefficient is specific to the first term of a polynomial when expressed in standard form.
Constant terms are specifically characterized by the absence of variables, just a number.
Linear terms are defined by the presence of the variable x.

Coefficients of Specific Terms

The coefficient of a linear term is the numerical factor associated with the x variable.
The quadratic term includes the variable x squared, and its coefficient is the numerical factor present in this term.

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Description

Test your understanding of polynomial concepts with these flashcards focused on standard form, terms, and types of polynomials such as monomials and binomials. Perfect for students looking to master polynomial definitions and terminology.