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

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 91

Factor completely, or state that the polynomial is prime. $$2 x^{3}-8 a^{2} x+24 x^{2}+72 x$$

Short Answer

Expert verified
The completely factored form of the given polynomial is \(2x[(x - 2a + 6)^2]\)

Step by step solution

01

Identify the common factor

To factor the polynomial, first we need to identify the greatest common factor (GCF) of all the terms. In this case, the GCF of all terms is \(2x\).
02

Factor out the common factor

Factor out the common factor, which gives: \(2x(x^2 - 4a^2 + 12x + 36)\)
03

Further factoring

Next, it can be identified that the expression inside the brackets is a quadratic equation and can be factored. This leads to \(2x[(x - 2a)^2 + 12(x - 2a) + 36]\)
04

Complete the square

The expression inside the brackets is a perfect square trinomial and can be further written as a square of a binomial. Completing the square we get: \(2x[(x - 2a + 6)^2]\)

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

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{5(x+2)}{2 x-14}, \text { for } x=10$$

$$\text { factor completely.}$$ $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$

Find the intersection of the sets. $$\\{1,3,5,7\\} \cap\\{2,4,6,8,10\\}$$

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

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-\pi \geq-\pi$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.