/*! 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 101 Evaluate each expression for \(x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 101

Evaluate each expression for \(x=3 .\) See Sections 1.3 and 1.6. $$ 4 x^{3}-5 x^{2}+2 x-5 $$

Short Answer

Expert verified
64

Step by step solution

01

- Substitute the Value of x

Replace every occurrence of x in the expression with 3. The expression becomes: 4(3)^3 - 5(3)^2 + 2(3) - 5
02

- Evaluate the Cubic Term

Calculate the value of the cubic term 4(3)^3 = 4(27) = 108
03

- Evaluate the Square Term

Calculate the value of the square term -5(3)^2 = -5(9) = -45
04

- Evaluate the Linear Term

Calculate the value of the linear term 2(3) = 6
05

- Combine All Terms

Add all the calculated values together to get the final result 108 - 45 + 6 - 5 = 64

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
Evaluating algebraic expressions often starts with the process called substitution. In simple terms, substitution means replacing each instance of a variable in an expression with a specific value.
In this exercise, we are given the expression \(4x^3 - 5x^2 + 2x - 5\) and need to substitute \(x\) with 3.
Let's substitute 3 in place of \(x\):
The expression becomes \(4(3)^3 - 5(3)^2 + 2(3) - 5\).
With substitution, the abstract becomes concrete, making calculations straightforward.
Cubic Term
The cubic term in an algebraic expression is any term where the variable is raised to the power of three. This term is crucial because it can greatly impact the total value.
In our expression, the cubic term is \(4x^3\). With our substitution, it becomes \(4(3)^3\).
To solve it, calculate the cube of 3, which is 27, and then multiply by 4:
\[4 \times 27 = 108\]
This step simplifies the cubic term's contribution to the expression.
Square Term
A square term in algebra involves a variable raised to the power of two. It is often simpler than cubic terms but still significant.
In our case, the square term is \(-5x^2\). Substituting 3 for \(x\), we get \(-5(3)^2\).
First, compute the square of 3, resulting in 9, then multiply by -5:
\[-5 \times 9 = -45\]
This calculation shows the square term's effect on the overall expression.
Linear Term
Linear terms are the simplest to evaluate in an algebraic expression. They involve the variable raised to the first power.
Our given linear term here is \(2x\). By substituting \(x\) with 3, we get \(2(3)\).
This straightforward calculation results in:
\[2 \times 3 = 6\]
Even though it's simple, the linear term still affects the final result.
Now combine it with the cubic and square terms to see the overall impact on the original expression.

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

Find each product. $$ \left(\frac{2}{3}+r\right)\left(\frac{2}{3}-r\right) $$

Find each product. $$ (-2 k+1)\left(8 k^{2}+9 k+3\right) $$

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(9^{-1} z^{-2} x\right)^{-1}\left(4 z^{2} x^{4}\right)^{-2}}{\left(5 z^{-2} x^{-3}\right)^{2}} $$

Use scientific notation to calculate the answer to each problem. Write answers in scientific notation. $$ \frac{0.00000072(0.00023)}{0.000000018} $$

In theory there are \(1 \times 10^{9}\) possible Social Security numbers. The population of the United States is about \(3 \times 10^{8} .\) How many Social Security numbers are available for each person? (Source: U.S. Census Bureau.)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

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.