Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 4+5(x-7)3, for x =9
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 1, Problem 10
In Exercises 1–10, factor out the greatest common factor. x2(2x+5)+17(2x+5)
Verified step by step guidance1
Identify the common factor in the terms of the expression. Notice that both terms, \(x^2(2x+5)\) and \(17(2x+5)\), share the binomial \((2x+5)\) as a common factor.
Factor out the common binomial \((2x+5)\) from the expression. This means rewriting the expression as \((2x+5)(\text{something})\).
Determine what remains in each term after factoring out \((2x+5)\). From the first term \(x^2(2x+5)\), \(x^2\) remains. From the second term \(17(2x+5)\), \(17\) remains.
Combine the remaining terms into a single binomial. After factoring out \((2x+5)\), the expression becomes \((2x+5)(x^2 + 17)\).
Verify your result by distributing \((2x+5)\) back into \((x^2 + 17)\) to ensure it matches the original expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Greatest Common Factor (GCF)
The Greatest Common Factor is the largest expression that divides two or more terms without leaving a remainder. In algebra, identifying the GCF is crucial for simplifying expressions and factoring polynomials. For example, in the expression x^2(2x+5) + 17(2x+5), the GCF is (2x+5), as it is common to both terms.
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Graphs of Common Functions
Factoring
Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. This is essential in algebra for simplifying equations and solving for variables. In the given expression, factoring out the GCF allows us to rewrite it in a more manageable form.
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Polynomial Expressions
Polynomial expressions are mathematical expressions that consist of variables raised to whole number exponents and their coefficients. They can be added, subtracted, multiplied, and factored. Understanding how to manipulate polynomial expressions is fundamental in algebra, as it forms the basis for solving equations and analyzing functions.
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Related Practice
Textbook Question
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x3+5x2−8x+9)+(17x3+2x2−4x−13)
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Textbook Question
Rewrite each expression without the absolute value bars. |√2-1|
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Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x2-3(x-y), for x=8 and y=2
Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16
Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+√25
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