/*! 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 106 Factor completely. $$7 x^{4}+3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 106

Factor completely. $$7 x^{4}+34 x^{2}-5$$

Short Answer

Expert verified
The fully factorized form of the expression \(7x^{4}+34x^{2}-5\) is \((x - x1) (x - x2) (x - x3) (x - x4)\), where \(x1\), \(x2\), \(x3\), \(x4\) are the four solutions for x found in steps 5 and 6.

Step by step solution

01

Recognize the disguised quadratic form

Notice that the expression \(7x^{4}+34x^{2}-5\) can be written as a quadratic equation by treating \(x^{2}\) as a single variable, say \(y\). Then the equation becomes: \(7y^{2} + 34y - 5\).
02

Apply quadratic formula

To solve the quadratic equation, apply the quadratic formula \(y = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \), where a=7, b=34, c=-5. So the solutions for y should be: \(y = \frac{-34 \pm \sqrt{34^{2} - 4 * 7 * -5}}{2 * 7}\)
03

Solve for y

Calculate the expression in the quadratic formula, and get the two solutions for y, namely \(y1\) and \(y2\).
04

Substitute \(y = x^{2}\)

Remember at step 1, y was replaced with \(x^{2}\) as a way to utilize the quadratic formula. Now, substitute y back with \(x^{2}\), so the two solutions for \(x^{2}\) are \(y1\) and \(y2\).
05

Solve for x

Take the square root of both sides for solutions \(x^{2} = y1\) and \(x^{2} = y2\) to get the four solutions for x, denoted by \(x1\), \(x2\), \(x3\), \(x4\)
06

Write the factorized form

Finally, write down the fully factorized form of the original expression \(7x^{4}+34x^{2}-5\) based on the four solutions \(x1\), \(x2\), \(x3\), \(x4\)

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

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\).

Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone plans, long-distance telephone plans, or anything of interest. Be sure to bring in all the details for each option. At a second group meeting, select the two pricing situations that are most interesting and relevant. Using each situation, write a word problem about selecting the better of the two options. The word problem should be one that can be solved using a linear inequality. The group should turn in the two problems and their solutions.

What is a compound inequality and how is it solved?

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{4}}=-2$$

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.