Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 6x2−6x−12
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 75
Add or subtract terms whenever possible.
Verified step by step guidance1
Identify the like terms in the expression. Both terms have the fifth root of 2, which can be written as \(4 \sqrt[5]{2}\) and \(3 \sqrt[5]{2}\).
Since the radical parts are the same (\(\sqrt[5]{2}\)), you can combine the coefficients (the numbers in front of the radicals).
Add the coefficients: \(4 + 3 = 7\).
Write the combined expression as the sum of the new coefficient and the common radical: \(7 \sqrt[5]{2}\).
This is the simplified form of the expression after combining like terms.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Like Terms
Like terms are terms that have the same variable parts raised to the same powers. In expressions involving radicals, terms with the same radicand and root index can be combined by adding or subtracting their coefficients.
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Radical Expressions
A radical expression involves roots, such as square roots or fifth roots. Understanding how to interpret and manipulate radicals, including recognizing when two radicals are like terms, is essential for simplifying expressions.
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Simplifying Expressions
Simplifying expressions involves combining like terms and reducing expressions to their simplest form. This includes adding or subtracting coefficients of like radical terms to write the expression more concisely.
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Related Practice
Textbook Question
In Exercises 67–82, find each product. (9x+7y)2
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Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 9x3−9x
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Find each product :
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Textbook Question
Write each number in decimal notation without the use of exponents.
Textbook Question
State the name of the property illustrated. 6+(−4)=(−4)+6
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