Chapter 7: Q 72. (page 832)

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 factorization of $b^{2} + 14 b + 48$ is, $(b + 6) (b + 8)$ .

Step by step solution

Step 1. Given information

Given expression is $b^{2} + 14 b + 48$ .

Step 2. Find the last terms of the binomials

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

$(b) (b)$

Find two numbers that multiply to $48$ and add to $14$ .

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

Step 3. Factorization

Use $6$ and $8$ as the last terms of the binomials.

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

Step 4. Check

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

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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. Given information

Step 2. Find the last terms of the binomials

Step 3. Factorization

Step 4. Check

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In the following exercises, factor each trinomial of the formx2+bx+cb2+14b+48

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the binomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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