Textbook Question
Factor out the greatest common factor.
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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 1
Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)3 for x = 4
Verified step by step guidance1
Identify the given expression and the value of the variable: The expression is \(3 + 6(x - 2)^3\) and the value given is \(x = 4\).
Substitute the value of \(x\) into the expression: Replace every \(x\) with \(4\) to get \(3 + 6(4 - 2)^3\).
Simplify inside the parentheses first: Calculate \(4 - 2\) to simplify the expression to \(3 + 6(2)^3\).
Evaluate the exponent: Calculate \$2^3$ which means \(2 \times 2 \times 2\).
Multiply and add: Multiply the result of the exponent by \(6\), then add \(3\) 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.
Order of Operations
The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to correctly evaluate expressions. It follows the PEMDAS/BODMAS rule: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). This ensures consistent and accurate results.
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Evaluating Expressions with Variables
Evaluating an expression involves substituting the given value(s) for the variable(s) and simplifying the result. For example, replacing x with 4 in the expression 3 + 6(x - 2)^3 means calculating 3 + 6(4 - 2)^3 by first simplifying inside the parentheses, then applying exponents, and finally performing multiplication and addition.
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Exponents and Powers
Exponents indicate repeated multiplication of a base number. For instance, (x - 2)^3 means multiplying (x - 2) by itself three times. Understanding how to compute powers is essential for simplifying expressions correctly, especially when combined with other operations like addition and multiplication.
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Related Practice
Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √36
Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 7+5x, for x = 10
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Textbook Question
Find all numbers that must be excluded from the domain of each rational expression. 7/(x−3)
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