Q 149 In the following exercises, fact... [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 149 (page 849)

In the following exercises, factors completely
$5 x^{4} + 10 x^{3} - 75 x^{2}$

Short Answer

Expert verified

The factorization of $5 x^{4} + 10 x^{3} - 75 x^{2}$ is $5 x^{2} (x - 3) (x + 5)$

Step by step solution

Step 1. Given information

Given expression is $5 x^{4} + 10 x^{3} - 75 x^{2}$

Step 2. Find the Greatest Common Factor.

Greatest Common Factor is $5 x^{2}$

$5 x^{2} (x^{2} + 2 x - 15)$

Step 3. Find the last terms of the binomials.

Find the numbers that multiply to $- 15$ and add to $2$

Factors of -15	Sum of factors
-3, 5	-3 + 5 = 2

Step 4. Factorization

Use $- 3$ and $5$ as the last terms of the binomials.

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

Step 5. Check

$5 x^{2} (x - 3) (x + 5) = 5 x^{2} (x^{2} - 3 x + 5 x - 15) = 5 x^{4} + 10 x^{3} - 75 x^{2}$

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91影视

In the following exercises, factors completely
$5 x^{4} + 10 x^{3} - 75 x^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the Greatest Common Factor.

Step 3. Find the last terms of the binomials.

Step 4. Factorization

Step 5. Check

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91影视

In the following exercises, factors completely5x4+10x3-75x2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the Greatest Common Factor.

Step 3. Find the last terms of the binomials.

Step 4. Factorization

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factors completely
$5 x^{4} + 10 x^{3} - 75 x^{2}$