Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

1:35 minutes

Problem 12a

Textbook Question

Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.

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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 is a mathematical concept that represents the distance of a number from zero on the number line, regardless of direction. It is denoted by two vertical bars, for example, |x|. For any real number x, the absolute value is defined as |x| = x if x is greater than or equal to zero, and |x| = -x if x is less than zero.

Distance Between Two Numbers

The distance between two numbers on the number line can be calculated using the absolute value of their difference. Specifically, the distance d between two numbers a and b is given by the formula d = |a - b|. This formula ensures that the distance is always a non-negative value, reflecting the concept of distance in a geometric sense.

Evaluating Absolute Value

Evaluating absolute value involves substituting a specific number into the absolute value expression and simplifying it. For example, to evaluate |x| for x = -17, you would find that |-17| = 17. This process is essential for solving problems that require finding distances or magnitudes, as it translates the abstract concept of distance into a concrete numerical value.