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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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 9
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
Verified step by step guidance1
Substitute the given value of x = 9 into the algebraic expression 4 + 5(x - 7)^3. This gives: 4 + 5(9 - 7)^3.
Simplify the expression inside the parentheses. Calculate (9 - 7), which simplifies to 2. The expression now becomes: 4 + 5(2)^3.
Evaluate the exponentiation. Calculate 2^3, which means multiplying 2 by itself three times: 2 * 2 * 2. This simplifies to 8. The expression now becomes: 4 + 5(8).
Multiply the coefficient 5 by the result of the exponentiation. Calculate 5 * 8, which simplifies to 40. The expression now becomes: 4 + 40.
Add the constant 4 to the product 40. The final simplified expression is the result of this addition.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression 4 + 5(x - 7)³ combines constants and a variable, x, which is raised to a power. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which different operations should be performed to correctly evaluate an expression. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules ensures accurate calculations when evaluating expressions like 4 + 5(x - 7)³.
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Substitution
Substitution is the process of replacing a variable in an expression with a specific value. In this problem, we substitute x with 9 in the expression 4 + 5(x - 7)³. This step is crucial for evaluating the expression and obtaining a numerical result, allowing us to simplify and compute the final answer.
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Related Practice
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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Textbook Question
In Exercises 1–10, factor out the greatest common factor. x2(2x+5)+17(2x+5)
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Textbook Question
In Exercises 1–10, factor out the greatest common factor. x(2x+1)+4(2x+1)
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Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16
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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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