Chapter 6: Q. 372 (page 635)

Factor Trinomials of the Form $a x^{2} + b x + c$ ax using the ‘ $a c$ ’ Method
In the following exercises, factor.
$2 x^{2} + 9 x + 4$

Short Answer

Expert verified

By using $' a c'$ method, the factors of $2 x^{2} + 9 x + 4$ is $(2 x + 1) (x + 4)$

Step by step solution

Step 1. Given

The trinomial is $2 x^{2} + 9 x + 4$

To find the factors by using $' a c'$ method.

Step 2. Find the product ac

Find the product $a c$

$a c = 8$

Find two numbers that multiply to $a c$ and add to $b$ .

$(8) (1) = 8$

$8 + 1 = 9$

Step 3. Split the middle term

$2 x^{2} + 9 x + 4 = 2 x^{2} + 8 x + x + 4$

Factor by grouping

$= 2 x (x + 4) + 1 (x + 4)$

role="math" localid="1644672318322" $= (2 x + 1) (x + 4)$

Step 4. Check the answer

$(2 x + 1) (x + 4) = 2 x^{2} + 8 x + x + 4$

$= 2 x^{2} + 9 x + 4$

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.

Factor Trinomials of the Form $a x^{2} + b x + c$ ax using the ‘ $a c$ ’ Method
In the following exercises, factor.
$2 x^{2} + 9 x + 4$

Short Answer

Step by step solution

Step 1. Given

Step 2. Find the product ac

Step 3. Split the middle term

Step 4. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Factor Trinomials of the Form ax2+bx+cax using the ‘ac’ MethodIn the following exercises, factor.2x2+9x+4

Short Answer

Step by step solution

Step 1. Given

Step 2. Find the product ac

Step 3. Split the middle term

Step 4. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Factor Trinomials of the Form $a x^{2} + b x + c$ ax using the ‘ $a c$ ’ Method
In the following exercises, factor.
$2 x^{2} + 9 x + 4$