Textbook Question
Factor completely, or state that the polynomial is prime.
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 67
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17
Verified step by step guidance1
Identify the two numbers given: 2 and 17.
Recall that the distance between two numbers \(a\) and \(b\) on the number line can be expressed as the absolute value of their difference: \(\left| a - b \right|\).
Write the distance between 2 and 17 as \(\left| 2 - 17 \right|\) or equivalently \(\left| 17 - 2 \right|\).
Evaluate the expression inside the absolute value: calculate \(2 - 17\) or \(17 - 2\).
Find the absolute value of the result from the previous step to get the distance between the two numbers.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative and is denoted by vertical bars, e.g., |x|. For example, |−3| = 3 and |3| = 3.
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Distance Between Two Numbers
The distance between two numbers on the number line is the absolute value of their difference. This ensures the distance is always positive or zero, calculated as |a − b|, where a and b are the given numbers.
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Evaluating Absolute Value Expressions
To find the distance, substitute the numbers into the absolute value expression and simplify. For example, the distance between 2 and 17 is |2 − 17| = |−15| = 15, which gives the numerical distance.
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Related Practice
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