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Questions and Answers
What is a polynomial expression?
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?
What is a monomial?
A polynomial expression generated using ONLY the multiplication operator.
Define a binomial.
Define a binomial.
A polynomial expression written as a sum of two monomial terms.
What is a trinomial?
What is a trinomial?
What does a polynomial represent?
What does a polynomial represent?
What is the greatest common factor?
What is the greatest common factor?
What is a prime number?
What is a prime number?
Define a composite number.
Define a composite number.
What is a prime polynomial expression?
What is a prime polynomial expression?
What does factoring do?
What does factoring do?
What is the degree of a polynomial?
What is the degree of a polynomial?
Define a coefficient.
Define a coefficient.
What is a constant term?
What is a constant term?
What is a quadratic expression?
What is a quadratic expression?
If ab = 0, then a = 0 or b = 0.
If ab = 0, then a = 0 or b = 0.
What is the axis of symmetry?
What is the axis of symmetry?
Define vertex in the context of a quadratic function.
Define vertex in the context of a quadratic function.
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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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