Q 7.73 Factor completely:聽15n3-85n2+10... [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 7.73 (page 843)

Factor completely: $15 n^{3} - 85 n^{2} + 100 n$

Short Answer

Expert verified

The factorization of the expression $15 n^{3} - 85 n^{2} + 100 n$ is $5 n (3 n - 5) (n - 4)$

Step by step solution

Step 1. Given information

Given expression is $15 n^{3} - 85 n^{2} + 100 n$

Step 2. Find the Greatest Common Factor

Greatest Common Factor is $5 n$

$15 n^{3} - 85 n^{2} + 100 n = 5 n (3 n^{2} - 17 n + 20)$

Step 3. Find the product of a×c

$a 脳 c = 3 脳 20 = 60$

Step 4. Find the last terms of the binomials.

Find numbers that multiply to $60$ and add to $- 17$

Factors of $60$	Su,m of factors
-5, -12	-5 + (-12) = -17

Step 5. Factorization

Use $- 5$ and $- 12$ as the last terms of the binomials.

$5 n (3 n^{2} - 5 n - 12 n + 20) = 5 n (n (3 n - 5) - 4 (3 n - 5)) = 5 n (3 n - 5) (n - 4)$

Step 6. Check

$5 n (3 n - 5) (n - 4) = 5 n (3 n^{2} - 5 n - 12 n + 20) = 5 n (3 n^{2} - 17 n + 20) = 15 n^{3} - 85 n^{2} + 100 n$

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91影视

Factor completely: $15 n^{3} - 85 n^{2} + 100 n$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the Greatest Common Factor

Step 3. Find the product of a×c

Step 4. Find the last terms of the binomials.

Step 5. Factorization

Step 6. Check

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91影视

Factor completely:15n3-85n2+100n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the Greatest Common Factor

Step 3. Find the product of a×c

Step 4. Find the last terms of the binomials.

Step 5. Factorization

Step 6. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Factor completely: $15 n^{3} - 85 n^{2} + 100 n$