/*! 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 6 Divide as indicated. Check each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 6

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{x^{2}-2 x-24}{x+4}$$

Short Answer

Expert verified
The quotient for the division \(\frac{x^{2}-2 x-24}{x+4}\) is \(x-6\) with no remainder.

Step by step solution

01

Polynomial Long Division

Set up the division, treating it like long division. Write \(x^{2}-2 x-24\) divided by \(x+4\). Begin by dividing \(x^{2}\) by \(x\), yielding \(x\). Multiply \(x+4\) by \(x\) to get \(x^{2}+4x\), and subtract this from the original dividend \(x^{2}-2 x-24\), which gives \(-6x - 24\).
02

Continue Division

Now, divide \(-6x\) by \(x\), yielding \(-6\). Multiply \(x+4\) by \(-6\) to get \(-6x - 24\), subtract this from the \(-6x - 24\) above, yielding \(0\). Since we obtained \(0\), it means we have no remainder.
03

Check the Results

We can always check the results by multiplying the divisor and the quotient and making sure that it equals the original polynomial. This yields \(x(x+4) - 6(x+4) = x^{2}-2 x-24\), which confirms that the division was carried out correctly.

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!

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

In Exercises \(100-103,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{12 x^{3}-6 x}{2 x}=6 x^{2}-6 x$$

In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural Number. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.2 \times 10^{6}\right)\left(8.7 \times 10^{-2}\right)}{\left(2.9 \times 10^{6}\right)\left(3 \times 10^{-3}\right)}$$

In Exercises \(100-103,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a polynomial in \(x\) of degree 6 is divided by a monomial in \(x\) of degree \(2,\) the degree of the quotient is 4

In Exercises \(79-82,\) simplify each expression. $$\left(\frac{9 x^{3}+6 x^{2}}{3 x}\right)-\left(\frac{12 x^{2} y^{2}-4 x y^{2}}{2 x y^{2}}\right)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.