/*! 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 18 (a) factor out the greatest comm... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 18

(a) factor out the greatest common factor. Identify any prime polynomials. (b) check. $$ 21 p-56 w $$

Short Answer

Expert verified
GCF is 7, factored form is \(7(3p - 8w)\), and \(3p - 8w\) is prime.

Step by step solution

01

- Identify the Greatest Common Factor (GCF)

Determine the GCF of the coefficients 21 and 56. The GCF is 7 because 7 is the largest number that can divide both 21 and 56.
02

- Factor Out the GCF

Factor out the GCF (7) from the expression. This means we divide each term by 7 and place the 7 outside a set of parentheses: \(21p - 56w = 7(3p - 8w)\).
03

- Identify Prime Polynomials

Check whether the polynomial inside the parentheses, \(3p - 8w\), can be factored further. Since 3 and 8 have no common factors other than 1, and the polynomial is already in its simplest form, \(3p - 8w\) is a prime polynomial.
04

- Verify the Factoring

Multiply the factored expression back to confirm that it returns the original expression: \[ 7(3p - 8w) = 21p - 56w \]. The original expression is recovered, confirming that the factoring is correct.

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.

greatest common factor
To start factoring a polynomial, the first step is to identify the Greatest Common Factor (GCF). The GCF is the largest number that can divide each term in the polynomial without leaving a remainder. This helps simplify the polynomial by

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

An expression is \((x-4)(x-3)\). Evaluate this expression when \(x=4\).

The formula for density, \(d\), is \(d=\frac{m}{v}\), where \(m\) is the mass and \(v\) is the volume. The density of a steel sphere is \(7.85 \frac{\mathrm{g}}{\mathrm{cm}^{3}}\), and its mass is \(5 \times 10^{2} \mathrm{~g}\). Solve the formula for \(v\), and find the volume of this sphere. Round to the nearest whole number.

Factor completely. Identify any prime polynomials. $$ 27 h^{3}-k^{3} $$

The width of a rectangle is \(13 \mathrm{ft}\) less than twice its length. Its area is \(45 \mathrm{ft}^{2}\).

Solve. $$ (x-6)(x-6)=0 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure 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.