/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 50 Evaluate each expression. See Ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 50

Evaluate each expression. See Example 2 and \(3 .\) \(x^{2}-x+7\) for a. \(x=6\) b. \(x=-2\)

Short Answer

Expert verified
For \( x=6 \), the expression evaluates to 37. For \( x=-2 \), it evaluates to 13.

Step by step solution

01

Substitute and evaluate for x=6

First, we substitute the given value of \( x = 6 \) into the expression \( x^2 - x + 7 \). This becomes \( 6^2 - 6 + 7 \). Calculate: \( 6^2 = 36 \), so the expression is now \( 36 - 6 + 7 \). Next, simplify: \( 36 - 6 = 30 \), and then \( 30 + 7 = 37 \). Thus, the value of the expression for \( x = 6 \) is 37.
02

Substitute and evaluate for x=-2

Now, substitute \( x = -2 \) into the expression \( x^2 - x + 7 \). This gives us \( (-2)^2 - (-2) + 7 \). Calculate: \( (-2)^2 = 4 \), so the expression is \( 4 - (-2) + 7 \). Next, recognize that \( -(-2) = +2 \), thus it becomes \( 4 + 2 + 7 \). Finally, add these together: \( 4 + 2 = 6 \), then \( 6 + 7 = 13 \). Therefore, the value of the expression for \( x = -2 \) is 13.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution Method
The substitution method is an essential approach in algebra where you replace a variable in an expression with a given value. This makes the operation straightforward and allows for evaluating expressions accurately. To use this method:
  • Take the algebraic expression and identify the variable you are substituting.
  • Replace each instance of this variable with the given number.
  • Follow the order of operations to simplify the expression and find the result.
For example, in the expression \( x^2 - x + 7 \), if we substitute \( x = 6 \), we re-calculate each term where \( x \) appears by replacing it with \( 6 \). This is an invaluable method for finding specific values of algebraic expressions, especially in polynomial expressions.
Evaluating Algebraic Expressions
Evaluating an algebraic expression involves finding the value of the expression for given variable values. It's a skill that's essential for solving many algebra problems. Here's how it typically works:
  • First, substitute the given value for the variable into the expression.
  • Next, perform the operations following the standard mathematical order: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Using the expression \( x^2 - x + 7 \), suppose \( x \) is given as \(-2\). By substituting and evaluating step-by-step, you can clearly see how each operation transforms the expression into a numerical answer. Evaluating algebraic expressions is straightforward but requires careful attention to detail to ensure accuracy.
Polynomial Expressions
Polynomial expressions are a key component in algebra and consist of coefficients, variables, and exponents combined through operations such as addition and subtraction. They can look like \( x^2 - x + 7 \), where this expression is a simple polynomial with a degree of 2 due to the highest power of \( x \), which is 2.Features of polynomial expressions include:
  • Coefficients: Numbers multiplied by the variable, like \( 1x \) in \( -x \), where \( -1 \) is the coefficient.
  • Terms: Each part of the expression separated by addition or subtraction; in \( x^2 - x + 7 \), there are three terms.
  • Constant: A term without a variable, like \( 7 \) in this expression.
Polynomial expressions are fundamental in various mathematical calculations, from simple evaluations to complex calculus problems. Understanding their structure helps in simplifying, evaluating, and manipulating them to solve algebraic equations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain why the vertical form used in algebra to multiply \(2 x^{2}+3 x+1\) and \(3 x+2\) is similar to the vertical form used in arithmetic to multiply 231 and \(32 .\)

Perform each division. $$ \frac{3 b^{2}+11 b+6}{3 b+2} $$

Perform each division. $$ \left(x^{2}+10 x+30\right) \div(x+6) $$

Perform each division. $$ \frac{9 a^{4} b^{3}-16 a^{3} b^{4}}{12 a^{2} b} $$

Perform each division. $$ \frac{-65 r s^{2}}{15 r^{2} s^{5}} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.