Chapter 6: Q. 13 (page 572)

In the following exercises, factor the greatest common factor from each polynomial.
$3 x^{2} + 6 x - 9$

Short Answer

Expert verified

The factored form is $\begin{array}{rcl} 3 (x^{2} + 2 x - 3) \end{array}$ .

Step by step solution

Step 1. Given Information

The polynomial is $3 x^{2} + 6 x - 9$ .

Step 2. Find the GCF of the terms

Factor each of the terms in the given expression.

$3 x^{2} = 3 \cdot x \cdot x 6 x = 3 \cdot 2 \cdot x 9 = 3 \cdot 3$

From the obtained factors, it is observed that the common factor is 3.
So, the GCF of the terms of the given expression is 3.

Step 3. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, 3.

$3 \cdot x^{2} + 3 \cdot 2 x - 3 \cdot 3 = 3 (x^{2} + 2 x - 3)$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

$3 \cdot x^{2} + 3 \cdot 2 x - 3 \cdot 3 = 3 (x^{2} + 2 x - 3)$

Step 4. Check

Multiply the obtained factors.

$\begin{array}{rcl} 3 (x^{2} + 2 x - 3) & = & 3 \cdot x^{2} + 3 \cdot 2 x - 3 \cdot 3 \\ = & 3 x^{2} + 6 x - 9 \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

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 the greatest common factor from each polynomial.
$3 x^{2} + 6 x - 9$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the GCF of the terms

Step 3. Rewrite the given expression

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Geometry

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor the greatest common factor from each polynomial. 3x2+6x-9

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the GCF of the terms

Step 3. Rewrite the given expression

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Geometry

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor the greatest common factor from each polynomial.
$3 x^{2} + 6 x - 9$