Domanda del libro di testo
Evaluate each exponential expression in Exercises 1–22.
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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 12
In Exercises 11–16, factor by grouping. x3−3x2+4x−12
Guida verificata passo dopo passo1
Group the terms into two pairs: \( (x^3 - 3x^2) + (4x - 12) \).
Factor out the greatest common factor (GCF) from each group: \( x^2(x - 3) + 4(x - 3) \).
Notice that \( (x - 3) \) is a common factor in both terms. Factor \( (x - 3) \) out: \( (x - 3)(x^2 + 4) \).
Verify the factorization by distributing \( (x - 3) \) back into \( (x^2 + 4) \) to ensure it equals the original expression.
The expression is now factored as \( (x - 3)(x^2 + 4) \). This is the final factored form.
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Factoring by Grouping
Factoring by grouping is a method used to factor polynomials by rearranging and grouping terms in pairs. This technique involves identifying common factors in each group, allowing for the extraction of a common binomial factor. It is particularly useful for polynomials with four or more terms, as it simplifies the expression into a product of simpler polynomials.
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04:36
Factor by Grouping
Common Factors
A common factor is a number or variable that divides two or more terms without leaving a remainder. In the context of polynomials, identifying common factors within grouped terms is essential for simplifying the expression. Recognizing these factors allows for the extraction of a binomial or monomial, which is a crucial step in the factoring process.
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5:57Graphs of Common Functions
Polynomial Expressions
Polynomial expressions are mathematical expressions that consist of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Understanding the structure of polynomials, including their degree and coefficients, is vital for applying factoring techniques. In the given expression, recognizing the degree and the arrangement of terms aids in effectively applying the grouping method.
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05:09Introduction to Algebraic Expressions
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