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Use set-builder notation to describe each set. See Example 2. (More than one description is possible.) {2, 4, 6, 8}
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 21
Write each rational expression in lowest terms. See Example 2. (8x² + 16x) / 4x²
Guida verificata passo dopo passo1
Start by writing the given rational expression as a fraction: \(\frac{8x^{2} + 16x}{4x^{2}}\).
Factor the numerator by taking out the greatest common factor (GCF). For \(8x^{2} + 16x\), the GCF is \$8x$, so rewrite the numerator as \(8x(x + 2)\).
Rewrite the expression with the factored numerator: \(\frac{8x(x + 2)}{4x^{2}}\).
Factor the denominator if possible. Here, \$4x^{2}$ is already factored as \(4 \cdot x^{2}\).
Simplify the fraction by dividing both numerator and denominator by their common factors. Identify and cancel out the common factors step-by-step.
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Factoring Polynomials
Factoring involves rewriting a polynomial as a product of its factors. For example, 8x² + 16x can be factored by taking out the greatest common factor (GCF), which is 8x, resulting in 8x(x + 2). Factoring simplifies expressions and is essential for reducing rational expressions.
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Percorso guidato
6:08
Factoring
Simplifying Rational Expressions
A rational expression is a fraction where the numerator and denominator are polynomials. Simplifying involves factoring both parts and canceling common factors. This process reduces the expression to its lowest terms, making it easier to work with or interpret.
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Percorso guidato
2:58Rationalizing Denominators
Greatest Common Factor (GCF)
The GCF is the largest factor shared by two or more terms or polynomials. Identifying the GCF helps in factoring expressions and simplifying rational expressions by canceling common factors in numerator and denominator.
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Percorso guidato
6:08Factoring
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