Domanda del libro di testo
In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x2−5
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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 1
Factor out the greatest common factor.
Guida verificata passo dopo passo1
Identify the greatest common factor (GCF) of the coefficients 18 and 27. To do this, find the largest number that divides both 18 and 27 evenly.
Determine if there is a common variable factor in the terms. Since the terms are 18x and 27, check if both terms contain the variable 'x'.
Write the GCF based on the common numerical factor and any common variable factors found. In this case, it will be a number since only one term has 'x'.
Express each term as a product of the GCF and another factor. For example, write 18x as (GCF) times something, and 27 as (GCF) times something else.
Factor out the GCF from the entire expression and write the factored form as \(\text{GCF} \left( \text{remaining factor of first term} + \text{remaining factor of second term} \right)\).
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Greatest Common Factor (GCF)
The Greatest Common Factor is the largest factor that divides two or more numbers or expressions without leaving a remainder. Finding the GCF helps simplify expressions by factoring out common terms, making further operations easier.
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Graphs of Common Functions
Factoring Out the GCF
Factoring out the GCF involves rewriting an expression as a product of the GCF and another simplified expression. This process reduces the expression to a simpler form and is often the first step in factoring polynomials.
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Factoring Algebraic Expressions
Factoring algebraic expressions means expressing them as a product of simpler expressions. Recognizing common factors, such as numbers and variables with the smallest exponents, is essential to break down expressions effectively.
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05:09Introduction to Algebraic Expressions
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