Q 7.63. Factor completely:聽5x3+15x2-20x... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q 7.63. (page 838)

Factor completely: $5 x^{3} + 15 x^{2} - 20 x$

Short Answer

Expert verified

The factorization of $5 x^{3} + 15 x^{2} - 20 x$ is,localid="1649201372468" $5 x (x - 1) (x + 4)$ .

Step by step solution

Step 1. Given information

Given expression is $5 x^{3} + 15 x^{2} - 20 x$ .

Step 2. Find the greatest common factor

Greatest common factor is $5 x$ .

$5 x^{3} + 15 x^{2} - 20 x = 5 x (x^{2} + 3 x - 4)$

Step 3. Find Binomial, trinomial, or more than three terms

It is a trinomial.

So 鈥渦ndo FOIL.鈥�

$5 x (x) (x)$

Find two numbers that multiply to $- 4$ and add to $3$ .

Factors of -4	Sum of factors
-1, 4	-1 + 4 = 3*
-2, 2	-2 + 2 = 0
-4, 1	-4 + 1 = -3

Step 4. Factorization

Use $- 1$ and $4$ as the last terms of the trinomials.

$5 x (x^{2} + 3 x - 4) = 5 x (x - 1) (x + 4)$

Step 5. Check

$5 x (x - 1) (x + 4) = 5 x (x^{2} - 1 x + 4 x - 4) = 5 x (x^{2} + 3 x - 4) = 5 x^{3} + 15 x^{2} - 20 x$

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Factor completely: $5 x^{3} + 15 x^{2} - 20 x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the greatest common factor

Step 3. Find Binomial, trinomial, or more than three terms

Step 4. Factorization

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Factor completely:5x3+15x2-20x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the greatest common factor

Step 3. Find Binomial, trinomial, or more than three terms

Step 4. Factorization

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor completely: $5 x^{3} + 15 x^{2} - 20 x$