Domanda del libro di testo
Use an inequality symbol to write each statement. 5 is greater than or equal to 5.
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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 85
Factor each polynomial completely. See Example 6. 4m²p - 12mnp + 9n²p
Guida verificata passo dopo passo1
Identify the greatest common factor (GCF) of all the terms in the polynomial \(4m^{2}p - 12mnp + 9n^{2}p\). Look for common variables and coefficients shared by each term.
Factor out the GCF from the polynomial. This will simplify the expression and make it easier to factor the remaining quadratic expression inside the parentheses.
Focus on the quadratic expression inside the parentheses after factoring out the GCF. Recognize that it is a trinomial of the form $ax^{2} + bx + c$, where the variables are \(m\) and \(n\).
Use the method of factoring trinomials (such as the perfect square trinomial or the product-sum method) to factor the quadratic expression inside the parentheses completely.
Write the fully factored form by combining the GCF factored out initially with the factored form of the quadratic expression inside the parentheses.
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Factoring Polynomials
Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials or factors. This process helps simplify expressions and solve equations. Common methods include factoring out the greatest common factor, grouping, and recognizing special products like perfect square trinomials.
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Percorso guidato
6:08
Factoring
Greatest Common Factor (GCF)
The GCF is the largest expression that divides all terms of a polynomial without leaving a remainder. Identifying the GCF is the first step in factoring, as it simplifies the polynomial and makes further factoring easier. For example, in 4m²p - 12mnp + 9n²p, the GCF includes variables and coefficients common to all terms.
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Percorso guidato
6:08Factoring
Factoring Perfect Square Trinomials
A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, typically in the form a² ± 2ab + b² = (a ± b)². Recognizing this pattern allows quick factoring. In the given polynomial, after factoring out the GCF, the remaining trinomial may fit this pattern.
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Percorso guidato
6:08Factoring
Pratica correlata
Domanda del libro di testo
Add or subtract, as indicated. See Example 6. 5√3 - √3
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Simplify each complex fraction. See Examples 5 and 6. (1/(x + 1) − 1/x) / (1/x)
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Use an inequality symbol to write each statement. 13 - 3 is less than or equal to 10.
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Use an inequality symbol to write each statement. 5 + 0 is not equal to 0.
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Add or subtract, as indicated. See Example 6. 2√3 + 5√3
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