/*! 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 7 \(\left(12 a^{4}+6 a^{3}-3 a^{2}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 7

\(\left(12 a^{4}+6 a^{3}-3 a^{2}\right) \div 3\)

Short Answer

Expert verified
The simplified expression is \[4a^4 + 2a^3 - a^2\].

Step by step solution

01

Identify the Expression

The given expression is \((12a^4 + 6a^3 - 3a^2) \div 3\). This expression requires division of each term by 3.
02

Divide Each Term by 3

Divide every term inside the parentheses by 3: \[\frac{12a^4}{3}\, \frac{6a^3}{3}\, \text{and} \frac{3a^2}{3}\.\]
03

Simplify Each Term

Simplify each term separately: \ \[ \frac{12a^4}{3} = 4a^4 \] \[ \frac{6a^3}{3} = 2a^3 \] \[ \frac{3a^2}{3} = a^2 \]
04

Combine Simplified Terms

Combine all the simplified terms to form the final expression: \[4a^4 + 2a^3 - a^2\]

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.

polynomial division
Polynomial division is an essential skill in algebra. It involves dividing one polynomial by another polynomial or a constant. This process can be similar to long division with numbers, but it is applied to algebraic expressions. In our example, we need to divide the polynomial \(12a^4 + 6a^3 - 3a^2\) by the constant 3. To do this, we divide each term in the polynomial individually by 3. This makes the division simpler and prevents mistakes.

  • Understand what polynomial division is.
  • Learn to divide each term separately when dividing by a constant.
  • Simplify step-by-step to avoid errors.
simplifying expressions
Simplifying expressions is a crucial part of algebra. It helps to make complex expressions easier to work with. For our exercise, we break down the expression \(12a^4 + 6a^3 - 3a^2\) and divide each term by 3. After division, each term becomes simpler. For instance, \(12a^4\) divided by 3 turns into \(4a^4\). By simplifying each term, we get the modified polynomial \(4a^4 + 2a^3 - a^2\). Simplifying makes the expressions cleaner and prepares them for further operations.

  • Simplification involves breaking down complex terms.
  • Divide each part of the expression carefully.
  • Combine the simplified terms at the end.
basic algebra
Basic algebra involves fundamental operations such as addition, subtraction, multiplication, and division of algebraic expressions. In this exercise, we focus on division within the polynomial framework. Dividing a polynomial by a constant involves applying the division to each term separately. Once each term is divided, we combine the results to form a simplified expression. Basic algebraic techniques allow us to handle more complex operations down the line.

  • Master basic operations before moving to complex problems.
  • Ensure each step is followed correctly to avoid mistakes.
  • Combine your results accurately to form the final 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

The width of a rectangle is \(10 \mathrm{~cm}\) shorter than the length. a. If \(L=\) length, write a polynomial expression in \(L\) that represents the width, and draw a diagram of the rectangle. Do not include the units. b. Write a polynomial expression in \(L\) that represents the perimeter. c. Write a polynomial expression in \(L\) that represents the area.

\(\left(x^{2}+7 x-18\right) \div(x+9)\)

\(\left(k^{7}-5 k^{3}+100 k+20\right) \div 5\)

\(\left(4 p^{4}-16 p^{2}+60 p+20\right) \div(-4 p)\)

\(\left(x^{2}-10 x+16\right) \div(x-8)\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.