/*! 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 69 Factor completely, or state that... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 69

Factor completely, or state that the polynomial is prime. $$2 x^{4}-162$$

Short Answer

Expert verified
The complete factorization of the polynomial is \((x-9)(x+9)(x^2 + 81)\).

Step by step solution

01

Identify the Structure

Identify the structure of the polynomial. In this case, we have a difference of squares. The difference of squares is a special algebraic identity that is used to factorize a pair of perfect squares separated by subtraction. The expression takes the form \(a^2 - b^2\), which can be factored into \((a-b)(a+b)\). Here, \(a = x^{2}\) and \(b = 9^2 = 81\).
02

Factorize the Expression as Difference of Squares

Factorize the expression using the difference of squares identity. Applying it here, we get \((x^2 - 81) (x^2 + 81)\).
03

Factorize Again

The expression \(x^2 - 81\) can be factorized further since it is a difference of squares. Here, \(a = x\) and \(b = 9\). Using the difference of squares identity, we get \( (x-9)(x+9)\). The other component \(x^2 + 81\) cannot be factorized further as it is a sum of squares. Thus, the complete factorization of the binomial is \((x-9)(x+9)(x^2 + 81)\).

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

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$

When graphing the solutions of an inequality, what does a parenthesis signify? What does a square bracket signify?

What is a rational expression?

Explain why \(|x|<-4\) has no solution.

Explain how to solve \(x^{2}+6 x+8=0\) using factoring and the zero-product principle.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.