/*! 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 68 Find each product or quotient. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 68

Find each product or quotient. $$ \frac{-2 x t^{2}+8}{-4} $$

Short Answer

Expert verified
\( \frac{1}{2}xt^{2} - 2 \)

Step by step solution

01

Identify the expression to simplify

The given expression is \(\frac{-2xt^{2} + 8}{-4}\). We need to simplify this by dividing each term in the numerator by the denominator.
02

Simplify the first term of the numerator

The first term in the numerator is \(-2xt^{2}\). Divide this by the denominator \(-4\): \(\frac{-2xt^{2}}{-4}\). This simplifies to \( \frac{1}{2}xt^{2} \).
03

Simplify the second term of the numerator

The second term in the numerator is \8\. Divide this by the denominator \(-4\): \(\frac{8}{-4}\). This simplifies to \(-2\).
04

Combine the simplified terms

The simplified terms are \( \frac{1}{2}xt^{2} \) and \(-2\). Combine these to get the simplified expression: \(\frac{1}{2}xt^{2} - 2 \).

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.

Algebraic Fractions
Algebraic fractions are fractions that contain algebraic expressions in the numerator, the denominator, or both. They follow the same rules as regular fractions but can involve variables and more complex expressions. In the given exercise, the fraction is \(\frac{-2xt^{2} + 8}{-4}\). To simplify algebraic fractions, make sure to break down the components and handle each part of the expression carefully. Ensure every term in the numerator is divided by the denominator separately.
This helps maintain accuracy and prevents mistakes. Simplifying algebraic fractions is a core skill in algebra, which aids in further topics like solving equations and calculus.
Polynomial Division
Polynomial division involves dividing a polynomial by another polynomial or a monomial. In this exercise, we are dividing each term in the polynomial \(-2xt^{2} + 8\) by the monomial \-4\.
When dividing polynomials, follow these steps:
  • Divide each term of the numerator separately by the denominator.
  • Simplify each resulting term individually.
  • Combine the simplified terms to get the final result.

For example, in step-by-step terms:
First, divide \(-2xt^{2}\) by \-4\ to get \(\frac{1}{2}xt^{2}\).
Second, divide \(8\) by \-4\ to get \-2\.
Finally, combine them to get the answer: \(\frac{1}{2}xt^{2} - 2\).
This simplifies the polynomial into its simplest form.
Step-by-Step Solutions
Step-by-step solutions are essential for understanding how to approach and solve problems systematically. Here's a breakdown:
  • Step 1: Identify the expression: \(\frac{-2xt^{2} + 8}{-4}\).

  • Step 2: Simplify \(-2xt^{2}\) divided by \-4\, giving \(\frac{1}{2}xt^{2}\).

  • Step 3: Simplify \(8\) divided by \-4\, resulting in \-2\.

  • Step 4: Combine the results to get the final expression: \(\frac{1}{2}xt^{2} - 2\).

Breaking the problem down into small, manageable steps makes it less intimidating. Each step is clear and logical, ensuring you fully understand the process before moving on to the next part. This method improves comprehension and builds confidence in solving similar problems.

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

Simplify. $$ -\frac{1}{2} m\left(-\frac{1}{2} m\right)-\frac{1}{2} m-\frac{1}{2} m $$

Use an operation with signed numbers to solve each problem and identify the operation used. Highs and lows. The altitude of the peak of Mt. Everest, the highest point on earth, is \(29,028\) feet. The world's greatest known ocean depth of \(-36,201\) feet was recorded in the Marianas Trench (Rand McNally World Atlas). How many feet above the bottom of the Marianas Trench is a climber who has reached the top of Mt. Everest? (IMAGE CANT COPY)

Use an operation with signed numbers to solve each problem and identify the operation used. Explain why 0 is the only real number that does not have a multiplicative inverse.

Simplify. $$ 3(1-x y)-2(x y-5)-(35-x y) $$

Find each product or quotient. $$ (-4 y)(-4 y) $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics 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.