Textbook Question
In Exercises 5–8, find the degree of the polynomial. x2−4x3+9x−12x4+63
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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 7
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x2-6x+3, for x=7
Verified step by step guidance1
Substitute the given value of x (x = 7) into the algebraic expression x^2 - 6x + 3. This gives:
Simplify the first term by calculating the square of 7:
Simplify the second term by multiplying 6 by 7:
Combine the simplified terms into the expression:
Simplify the final expression by performing the subtraction and addition in order: and then add 3.
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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 x^2 - 6x + 3 consists of a quadratic term (x^2), a linear term (-6x), and a constant term (3). Understanding how to manipulate and evaluate these expressions is fundamental in algebra.
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Substitution
Substitution is the process of replacing a variable in an expression with a specific value. For the expression x^2 - 6x + 3, substituting x with 7 means replacing every instance of x in the expression with 7. This step is crucial for evaluating the expression and finding its numerical value.
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Evaluating Expressions
Evaluating an expression involves performing the necessary arithmetic operations to simplify it to a single numerical value. After substituting the variable, you will calculate the result by following the order of operations (PEMDAS/BODMAS). This ensures that you correctly handle exponents, multiplication, and addition in the right sequence.
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Related Practice
Textbook Question
Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∪ B.
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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
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Textbook Question
Evaluate each exponential expression in Exercises 1–22. (−3)0
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Textbook Question
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x2−6x+9)
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