Algebra 1 - Module 4 Flashcards

Questions and Answers

What is a polynomial expression?

An expression consisting of variables and coefficients (correct)

An expression with only two monomial terms

An expression that includes only multiplication

An expression with operations of addition, subtraction, multiplication, division, and non-negative integer exponents (correct)

What is a monomial?

A polynomial expression generated using ONLY the multiplication operator.

Define a binomial.

A polynomial expression written as a sum of two monomial terms.

What is a trinomial?

A polynomial expression written as a sum of three monomial terms. Signup and view all the answers

What does a polynomial represent?

A polynomial expression written as a sum of any number of monomial terms. Signup and view all the answers

What is the greatest common factor?

The highest number that divides exactly into two or more numbers. Signup and view all the answers

What is a prime number?

A positive integer greater than 1 whose only positive integer factors are 1 and itself. Signup and view all the answers

Define a composite number.

A positive integer greater than 1 that is not a prime number. Signup and view all the answers

What is a prime polynomial expression?

A polynomial expression that is not equivalent to 1 or -1 and cannot be factored further. Signup and view all the answers

What does factoring do?

It is the reverse process that 'undos' multiplication. Signup and view all the answers

What is the degree of a polynomial?

The largest exponent of all exponents on all terms of the polynomial. Signup and view all the answers

Define a coefficient.

A number multiplied by a variable in an algebraic expression. Signup and view all the answers

What is a constant term?

A term of a polynomial that consists only of a number that is not multiplied by a variable. Signup and view all the answers

What is a quadratic expression?

A polynomial expression of degree 2. Signup and view all the answers

If ab = 0, then a = 0 or b = 0.

True Signup and view all the answers

What is the axis of symmetry?

The line that divides a graph into two symmetrical pieces. Signup and view all the answers

Define vertex in the context of a quadratic function.

The point where the graph of a quadratic function and its axis of symmetry intersect. Signup and view all the answers

Study Notes

Polynomial Expressions

A polynomial expression consists of variables and coefficients, involving operations such as addition, subtraction, multiplication, division, and non-negative integer exponents.
Monomial: Built only from multiplication of terms, having one term.
Binomial: Sum of two monomials, resulting in two terms.
Trinomial: Sum of three monomials, leading to three terms.
General polynomial: Sum of any number of monomials, varying in number of terms.

Mathematical Concepts

Greatest Common Factor (GCF): The largest number that perfectly divides two or more numbers.
Prime Number: A positive integer greater than 1 with no divisors other than 1 and itself, making it indivisible by other integers.
Composite Number: A positive integer greater than 1 that has additional divisors beyond just 1 and itself; it can be evenly divided by several integers.

Polynomials and Properties

Prime Polynomial Expression: A polynomial that is neither equivalent to 1 or -1 and cannot be factored into products of lesser-degree polynomial factors.
Factoring: The process of determining expressions that multiply together to form the original polynomial, essentially reversing multiplication.
Degree of a Polynomial: The highest exponent found in any term of the polynomial, indicating its maximum power.

Key Terms

Coefficient: A numeric factor that multiplies a variable in an algebraic expression.
Constant Term: Part of a polynomial that is solely a numerical value, lacking a variable component.

Specialized Polynomial Types

Quadratic Expression: Specifically, a polynomial expression where the highest degree is 2, indicating its parabolic graphing characteristics.

Properties of Quadratics

Zero Product Property: Indicates that if the product of two factors equals zero, at least one of the factors must be zero.
Axis of Symmetry: A vertical line that bisects the graph of a quadratic function, located at x = -b/2a.
Vertex: The intersection point of the graph of a quadratic function and its axis of symmetry, crucial for graphing parabolas.

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Description

Test your knowledge of polynomial expressions in this Algebra 1 Module 4 flashcard quiz. Learn about key terms such as monomial, binomial, and the characteristics of polynomial expressions. Perfect for students wanting to solidify their understanding before exams.