Questions and Answers
What is a polynomial?
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?
A polynomial with two terms.
What is a trinomial?
Signup and view all the answers
What is an expression?
Signup and view all the answers
What is the degree of a polynomial?
Signup and view all the answers
What is the greatest common factor?
Signup and view all the answers
What does distributing mean in algebra?
Signup and view all the answers
What is the difference of two squares?
Signup and view all the answers
What is a perfect-square trinomial?
Signup and view all the answers
What is the degree of a monomial?
Signup and view all the answers
What is the standard form of a polynomial?
Signup and view all the answers
What is a perfect square?
Signup and view all the answers
What is the degree of a term?
Signup and view all the answers
What is area?
Signup and view all the answers
What does it mean to factor a polynomial?
Signup and view all the answers
What does factoring mean?
Signup and view all the answers
How does a trinomial work?
Signup and view all the answers
What does a standard form look like?
Signup and view all the answers
What are factors?
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!