Textbook Question
In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x2+11x+10)
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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 5
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2+3x, for x=8
Verified step by step guidance1
Step 1: Start with the given algebraic expression: .
Step 2: Substitute the given value of into the expression. This gives: .
Step 3: Simplify the first term, , which means multiplying 8 by itself.
Step 4: Simplify the second term, , which means multiplying 3 by 8.
Step 5: Add the results from Step 3 and Step 4 to find the value of the expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression x^2 + 3x consists of the variable x raised to the second power and multiplied by 3, which are combined using addition. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.
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Substitution
Substitution is the process of replacing a variable in an expression with a specific value. In the given problem, we substitute x with 8 in the expression x^2 + 3x. This step is crucial for evaluating the expression and obtaining a numerical result, which is a common practice in algebra.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. When evaluating the expression after substitution, following these rules is essential to arrive at the correct answer.
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Related Practice
Textbook Question
Evaluate each exponential expression in Exercises 1–22. −26
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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
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25
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Textbook Question
Evaluate each exponential expression in Exercises 1–22. (−3)0
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Textbook Question
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x2−6x+9)
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