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Questions and Answers
What is Standard Form?
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?
What is a Term in a polynomial?
Each monomial in a polynomial.
Define Monomials.
Define Monomials.
A number, a variable, or the product of a number and one or more variables (no + or - present).
What is a Binomial?
What is a Binomial?
What is a Trinomial?
What is a Trinomial?
What is a polynomial with 4 terms called?
What is a polynomial with 4 terms called?
What is the Degree of a polynomial?
What is the Degree of a polynomial?
What is a Constant?
What is a Constant?
What does Linear mean in polynomial terms?
What does Linear mean in polynomial terms?
What does Quadratic mean in polynomial terms?
What does Quadratic mean in polynomial terms?
What does Cubic mean in polynomial terms?
What does Cubic mean in polynomial terms?
What is a Coefficient?
What is a Coefficient?
What is a Leading Coefficient?
What is a Leading Coefficient?
What is a Constant Term?
What is a Constant Term?
What is a Linear Term?
What is a Linear Term?
What is the Coefficient of a Linear Term?
What is the Coefficient of a Linear Term?
What is a Quadratic Term?
What is a Quadratic Term?
What is the Coefficient of a Quadratic Term?
What is the Coefficient of a Quadratic Term?
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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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