/*! 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 20 Divide each polynomial by 3 \(x^... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 20

Divide each polynomial by 3 \(x^{2}\) $$ 24 x^{6}-12 x^{5}+30 x^{4} $$

Short Answer

Expert verified
8x^4 - 4x^3 + 10x^2

Step by step solution

01

- Write down the problem

Start by writing down the problem we need to solve: \( \frac{24x^{6} - 12x^{5} + 30x^{4}}{3x^{2}} \)
02

- Divide each term individually

Divide each term in the polynomial \(24x^{6} - 12x^{5} + 30x^{4}\) by \(3x^{2}\). Calculate: 1. \( \frac{24x^{6}}{3x^{2}} \) 2. \( \frac{12x^{5}}{3x^{2}} \) 3. \( \frac{30x^{4}}{3x^{2}} \)
03

- Simplify each fraction

Simplify each term from previous step: 1. \( \frac{24x^{6}}{3x^{2}} = \frac{24}{3} \times \frac{x^{6}}{x^{2}} = 8x^4 \) 2. \( \frac{12x^{5}}{3x^{2}} = \frac{12}{3} \times \frac{x^{5}}{x^{2}} = 4x^3 \) 3. \( \frac{30x^{4}}{3x^{2}} = \frac{30}{3} \times \frac{x^{4}}{x^{2}} = 10x^2 \)
04

- Combine the simplified terms

Combine the simplified terms: \(8x^4 - 4x^3 + 10x^2\)

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.

simplifying polynomials
When simplifying polynomials, it鈥檚 all about breaking down the expression into more manageable parts. A polynomial is an expression made up of adding and subtracting terms, with each term being a coefficient multiplied by a variable raised to a power. Simplifying polynomials often involves combining these like terms and performing basic algebraic operations. In our problem, the polynomial is 24x鈦� - 12x鈦� + 30x鈦�. Simplifying helps to make the expression easier to work with and provides a clearer view of the polynomial's behavior.
dividing terms individually
Dividing terms individually is a strategic method to handle complex polynomial division. It means you take each term in the polynomial and divide it separately by the divisor. In our exercise with the polynomial 24x鈦� - 12x鈦� + 30x鈦� divided by 3x虏, here鈥檚 how you would approach it:

1. Divide the first term: 24x鈦� by 3x虏.
2. Divide the second term: -12x鈦� by 3x虏.
3. Divide the third term: 30x鈦� by 3x虏.

By splitting the polynomial, the task becomes much simpler, making it easy to calculate and understand each step.
combining like terms
Combining like terms is crucial when simplifying expressions. Like terms in a polynomial are the terms that have the same variable raised to the same power. For instance, in the expression 24x鈦� - 12x鈦� + 30x鈦�, each term is distinct initially. But after dividing and simplifying, the result is 8x鈦� - 4x鲁 + 10x虏.

Here鈥檚 how you combine them:
  • Simplify each term individually.
  • Add or subtract the simplified terms to get a final, more compact expression.
This process makes the polynomial more straightforward and easier to use in further calculations or expressions.

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

Evaluate. $$ 1000(1.53) $$

List all positive integer factors of each number. $$ 18 $$

Write each number in scientific notation. $$ -0.01234 $$

Find each product. $$ p(3 p+7)(3 p-7) $$

In each polynomial, add like terms whenever possible. Write the result in descending powers of the variable. $$ -3 m^{5}+5 m^{5} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.