/*! 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 102 Suppose that a polynomial contai... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 102

Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.

Short Answer

Expert verified
Factoring by grouping for a polynomial with four terms involves splitting the polynomial into two groups, identifying common factors within each group, factoring out the common terms, and simplifying the resulting expressions. For example, a polynomial \(ax + ay + bz + bz\) can be factored to \(a(x + y) + 2bz\).

Step by step solution

01

Understand the Polynomial

The polynomial contains four terms. For example, consider a polynomial \(ax + ay + bz + bz\).
02

Group the Terms

Split the polynomial into two groups. Our polynomial can be split as follows: \((ax + ay) + (bz + bz)\).
03

Identify Common Factors

Next step is to identify the common factors within each group. In this case, \(a\) and \(b\) are common to the first and second groups respectively.
04

Factor the Groups

Factor out the common terms from each group, leading to: \(a(x + y) + b(z + z)\).
05

Simplify the Factored Polynomial

Simplify the factors. In this case, the simplified polynomial is \(a(x + y) + 2bz\).

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

Find all numbers that must be excluded from the domain of each rational expression. $$ \frac{7}{x-3} $$

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{3 x-9}{x^{2}-6 x+9} $$

Write each number in decimal notation. $$ 7.86 \times 10^{-4} $$

Use the product rule to simplify the expressions in Exercises \(7-16 .\) In Exercises \(11-16,\) assume that variables represent nonnegative real numbers. $$\sqrt{2 x} \cdot \sqrt{6 x}$$

Simplify each exponential expression $$ \left(\frac{4 a^{-5} b^{3}}{12 a^{3} b^{-5}}\right)^{0} $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.