Textbook Question
In Exercises 1–10, factor out the greatest common factor. 3x2+6x
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 3
In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x2−25)
Verified step by step guidance1
Identify the domain of a rational expression. The domain includes all real numbers except those that make the denominator equal to zero, as division by zero is undefined.
Write the denominator of the given rational expression: .
Set the denominator equal to zero to find the values that must be excluded: .
Factor the denominator using the difference of squares formula: .
Solve for the values of that make the denominator zero: gives , and gives . These are the values that must be excluded from the domain.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Expressions
A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding rational expressions is crucial because they can have restrictions on their domain, specifically where the denominator equals zero, as division by zero is undefined.
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Rationalizing Denominators
Domain of a Function
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational expressions, the domain excludes any values that make the denominator zero, as these values would lead to undefined expressions.
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3:51Domain Restrictions of Composed Functions
Factoring Polynomials
Factoring polynomials involves breaking down a polynomial into simpler components (factors) that, when multiplied together, yield the original polynomial. This is essential for identifying values that make the denominator zero, allowing us to determine which numbers must be excluded from the domain.
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07:30Introduction to Factoring Polynomials
Related Practice
Textbook Question
Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∩ B.
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Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 6x-y, for x=3 and y=8
Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2+3x, for x=8
Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. −√36
Textbook Question
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x
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