Chapter 7: Q 79 (page 832)

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$
$x^{2} - 8 x + 7$

Short Answer

Expert verified

The factorization of $x^{2} - 8 x + 7$ is, $(x - 1) (x - 7)$ .

Step by step solution

Step 1. Given information

Given expression is $x^{2} - 8 x + 7$ .

Step 2. Find the last terms of the binomials

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

$(x) (x)$

Find two numbers that multiply to $7$ and add to $- 8$ .

Factors of 7	Sum of factors
-1, -7	-1 + (-7) = -8

Step 3. Factorization

Use $- 1$ and $- 7$ as the last terms of the binomials.

$x^{2} - 8 x + 7 = (x - 1) (x - 7)$

Step 4. Check

$(x - 1) (x - 7) = x^{2} - x - 7 x + 7 = x^{2} - 8 x + 7$

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 $x^{2} + b x + c$
$x^{2} - 8 x + 7$

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

Applied Mathematics

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form x2+bx+cx2-8x+7

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

Applied Mathematics

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$
$x^{2} - 8 x + 7$