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Questions and Answers
What is the definition of an Algebraic Fraction?
What is the definition of an Algebraic Fraction?
- Quotient of Polynomials (correct)
- Product of Polynomials
- Difference of Polynomials
- Sum of Polynomials
What are Excluded Values Domain Restrictions?
What are Excluded Values Domain Restrictions?
Variable values that cause division by zero making the expression undefined
What is meant by the term Domain?
What is meant by the term Domain?
Set of values that can replace the variable
What are ZEROS in the context of rational equations?
What are ZEROS in the context of rational equations?
What are Extraneous Roots?
What are Extraneous Roots?
The expression $x³+y³$ can be factored as $(x+y)(x²−xy+y²)$. Fill in the blank: $x³+y³ = (x+y)(______)$
The expression $x³+y³$ can be factored as $(x+y)(x²−xy+y²)$. Fill in the blank: $x³+y³ = (x+y)(______)$
The expression $x³−y³$ can be factored as $(x−y)()$. Fill in the blank: $x³−y³ = (x−y)()$
The expression $x³−y³$ can be factored as $(x−y)()$. Fill in the blank: $x³−y³ = (x−y)()$
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Study Notes
Rational Expressions and Related Terms
- Algebraic Fraction: Defined as the quotient of two polynomials, representing a rational expression.
- Excluded Values: Specific variable values that lead to division by zero, rendering the expression undefined; crucial for determining valid domains.
- Domain: The complete set of permissible values that can substitute the variable within a rational expression.
Zeros and Roots
- Zeros: The values of the variable that result in the numerator of a rational equation equating to zero; identified using the Zero Product Property.
- Extraneous Roots: Solutions derived from altered equations that fail to satisfy the original equation; important to note that these roots may also be excluded values.
Polynomial Identities
- Sum of Cubes Formula: The expression (x³ + y³) factors into ((x + y)(x² - xy + y²)).
- Difference of Cubes Formula: The expression (x³ - y³) factors into ((x - y)(x² + xy + y²)).
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