Chapter 6: Q. 149E (page 590)

In the following exercises, factor each expression using any method $24 n^{2} + 20 n + 4$

Short Answer

Expert verified

The factors are $4 (2 n + 1) (3 n + 1)$

Step by step solution

Step 1. Given Information

The trinomial is $24 n^{2} + 20 n + 4$

Find factors using 'ac' method.

Step 2. Find GCF

Find GCF and factor it

GCF is 4

So, trinomial becomes $4 (6 n^{2} + 5 n + 1)$

Step 3. Find 'ac'

Compare the trinomial inside the parenthesis with $a x^{2} + b x + c$

So, $a = 6, b = 5, c = 1$

so, $a c = 6$

Find two number such as their product is 6 and sum is 5

So numbers are 2,3.

Step 4. Split the middle and factor trinomial by grouping

Split the middle term

$4 (6 n^{2} + 3 n + 2 n + 1)$

Factor it

$4 (3 n (2 n + 1) + 1 (2 n + 1)) 4 (2 n + 1) (3 n + 1)$

Step 5. Check

Multiply the factors $4 (2 n + 1) (3 n + 1)$

$4 (6 n^{2} + 2 n + 3 n + 1) 4 (6 n^{2} + 5 n + 1) 24 n^{2} + 20 n + 4$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, factor each expression using any method $24 n^{2} + 20 n + 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find GCF

Step 3. Find 'ac'

Step 4. Split the middle and factor trinomial by grouping

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each expression using any method24n2+20n+4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find GCF

Step 3. Find 'ac'

Step 4. Split the middle and factor trinomial by grouping

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each expression using any method $24 n^{2} + 20 n + 4$