Chapter 6: Q 64E (page 589)

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$b^{2} + 14 b + 48$

Short Answer

Expert verified

The factors are $(b + 6) (b + 8)$ .

Step by step solution

Step 1. Writing the expression

Write the factors as two binomials with first terms $b$ .

localid="1644544130598" $(b) (b)$ .

Step 2. Finding the factors

We need to find two numbers whose product is $48$ and sum is $14$ .

Factors of $48$	Sum of factors
$1, 48$	$49$
$2, 24$	$26$
$3, 16$	$19$
$4, 12$	$16$
$6, 8$	14

Thus $6, 8$ are the correct factors.

Thus, the factorization of the trinomiall is localid="1644542220674" $(b + 6) (b + 8)$ .

Step 3. Check

Multiply the factorization to get the trinomial again.

$(b + 6) (b + 8) = b^{2} + 8 b + 6 b + 48 (b + 6) (b + 8) = b^{2} + 14 b + 48$

Thus, the obtained factorization is correct.

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 trinomial of the form $x^{2} + b x + c$ .
$b^{2} + 14 b + 48$

Short Answer

Step by step solution

Step 1. Writing the expression

Step 2. Finding the factors

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Pure Maths

Geometry

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form x2+bx+c.b2+14b+48

Short Answer

Step by step solution

Step 1. Writing the expression

Step 2. Finding the factors

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Pure Maths

Geometry

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$b^{2} + 14 b + 48$