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Factor completely, or state that the polynomial is prime. 3x^4-12x^2
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 1, Problema 104
In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|
Guida verificata passo dopo passo1
Recall that the absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. So, for any number \(a\), \(|a| = \text{distance from zero}\).
Calculate the absolute value of the first number: \(|-20|\). Since \(-20\) is 20 units away from zero, \(|-20| = 20\).
Calculate the absolute value of the second number: \(|-50|\). Since \(-50\) is 50 units away from zero, \(|-50| = 50\).
Compare the two absolute values: \(20\) and \(50\). Determine which is greater, or if they are equal.
Based on the comparison, insert the correct symbol ($<$, $>$, or $=$) between \(| -20 |\) and \(| -50 |\) to make a true statement.
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Absolute Value
The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−20| equals 20, and |−50| equals 50, regardless of the original sign.
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Parabolas as Conic Sections Example 1
Comparison of Numbers
Comparing numbers involves determining their relative size using symbols like <, >, or =. After evaluating absolute values, you compare the resulting positive numbers to decide which inequality symbol correctly represents their relationship.
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Properties of Inequalities
Inequalities express the order between two values. Understanding that if one number is larger than another, the correct symbol is >, and if smaller, <, helps in correctly inserting the inequality symbol between expressions.
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