Podcast
Questions and Answers
What is a polynomial?
What is a polynomial?
What is a monomial?
What is a monomial?
An expression that can be written as a real number, a variable, or a product of a real number and one or more variables with non-negative powers.
What is a binomial?
What is a binomial?
A polynomial with two terms.
What is a trinomial?
What is a trinomial?
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What is an expression?
What is an expression?
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What is the degree of a polynomial?
What is the degree of a polynomial?
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What is the greatest common factor?
What is the greatest common factor?
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What does distributing mean in algebra?
What does distributing mean in algebra?
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What is the difference of two squares?
What is the difference of two squares?
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What is a perfect-square trinomial?
What is a perfect-square trinomial?
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What is the degree of a monomial?
What is the degree of a monomial?
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What is the standard form of a polynomial?
What is the standard form of a polynomial?
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What is a perfect square?
What is a perfect square?
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What is the degree of a term?
What is the degree of a term?
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What is area?
What is area?
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What does it mean to factor a polynomial?
What does it mean to factor a polynomial?
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What does factoring mean?
What does factoring mean?
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How does a trinomial work?
How does a trinomial work?
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What does a standard form look like?
What does a standard form look like?
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What are factors?
What are factors?
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Study Notes
Polynomials
- An algebraic expression composed of one or more terms, categorized as monomials, binomials, or trinomials.
Monomials
- Defined as expressions that can be a real number, variable, or a product of a real number and variables with nonnegative powers.
Binomials
- A specific type of polynomial that consists of exactly two terms.
Trinomials
- A polynomial that includes three distinct terms.
Expression
- Represents a collection of symbols that form a mathematical statement, such as 8 + 7.
Degree of Polynomial
- Refers to the exponent of the highest power present among its variables.
Greatest Common Factor (GCF)
- The largest factor that two or more numbers share in common, essential for simplifying expressions.
Distributing
- The process of multiplying a term outside the parentheses with each term inside the parentheses.
Difference of Two Squares
- Represents two perfect squares separated by a minus sign, expressed as a² - b² = (a+b)(a-b).
Perfect-Square Trinomial
- Formed by squaring a binomial, resulting in a trinomial of the format a² + 2ab + b² or a² - 2ab + b².
Degree of Monomial
- Calculated as the sum of the exponents of all variables within that monomial.
Standard Form of a Polynomial
- Arranged such that the degrees of its monomial terms decrease sequentially from left to right.
Perfect Square
- A number whose positive square root is a whole number, e.g., 1, 4, 9, 16.
Degree of Term
- Determined by summing the exponents of all variables in a specific term.
Area
- The measurement of space within a 3D object, calculated as A = length x width x height.
Factor a Polynomial
- A polynomial is in factored form if expressed as a product of monomial factors and prime factors, requiring at least two terms.
Factoring
- The process of breaking an expression down into simpler components, such as turning 6x² + 2x + 21x + 7 into (2x + 7)(3x + 1) after extracting the GCF.
How a Trinomial Works
- Typically comprises three terms, with one squared, plus one variable term, formulated by adding/subtracting others (e.g., a² + 3m + 4).
How Standard Form Looks
- A polynomial in standard form is arranged as follows: 4x² + 24x + 12.
Factors
- Essential components used to decompose a larger number into parts that divide evenly into it.
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Description
Test your understanding of polynomials with these flashcards designed for Algebra 1. Each card presents a key term related to polynomials, including definitions of monomials, binomials, and trinomials. Brush up on your algebra vocabulary and enhance your skills!