/*! 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 117 Write a polynomial that fits the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 117

Write a polynomial that fits the given description. Do not use a polynomial that appears in this section or in the Exercise Set. The polynomial has four terms and can be factored by grouping.

Short Answer

Expert verified
The polynomial needed is \( ax^3 + bx^2 + ax + b \), where \( a \) and \( b \) are any constants.

Step by step solution

01

Write a polynomial with four terms

We start by writing any polynomial of four terms. We do not worry about the factorization at this step, just about making sure we have exactly four terms. A possible polynomial could be \( ax^3 + bx^2 + ax + b \).
02

Factor the polynomial by grouping

We now attempt to factor the polynomial by grouping. This technique involves splitting the polynomial into two pairs and factoring out the GCF of each pair. Our polynomial can be grouped as follows: \( ax^3 + bx^2 + ax + b = (ax^3 + bx^2) + (ax + b) \). Now, we can factor out the GCF of each group, resulting in \( ax^2(x + b) + 1(x + b) \). We can see that the polynomial can indeed be factored by grouping.

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

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$-7 y^{3}+21 y^{2}-14 y$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$3 x^{4} y^{2}-3 x^{2} y^{2}$$

The second angle of a triangle measures three times that of the first angle's measure. The third angle measures \(80^{\circ}\) more than the first. Find the measure of each angle.

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$100 y^{2}+49$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$48 x^{4} y-3 x^{2} y$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

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.