Chapter 4: Q. 12 (page 209)

Use the Remainder Theorem to find the remainder when $f (x)$ is divided by $x - c$ . Then use the Factor Theorem to determine whether $x - c$ is a factor of $f (x)$ .
$f (x) = - 4 x^{3} + 5 x^{2} + 8; x + 3$

Short Answer

Expert verified

The remainder is $161$ and $x + 3$ is not a factor.

Step by step solution

Step 1. Given information.

The given function is,

$f (x) = - 4 x^{3} + 5 x^{2} + 8; x + 3$ .

Step 2. Using remainder theorem.

We know that if $f (x)$ is divided by $x - c$ then the remainder will be $f (c)$ .

Here $f (x)$ is divided by $x + 3$ , then the remainder is $f (- 3)$ that is

$f (- 3) = - 4 {(- 3)}^{3} + 5 {(- 3)}^{2} + 8 = - 4 (- 27) + 5 (9) + 8 = 108 + 45 + 8 = 161$

Therefore, the remainder is $161$ .

Step 3. Using factor theorem.

We know that if $x - c$ is the factor of the polynomial $f (x)$ then

$f (c) = 0$ ,

Here $c = - 3$ , then

$f (c) = f (- 3) = 161$

We observe that $f (- 3) \neq 0$ ,then $x + 3$ is not a factor.

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.

Use the Remainder Theorem to find the remainder when $f (x)$ is divided by $x - c$ . Then use the Factor Theorem to determine whether $x - c$ is a factor of $f (x)$ .
$f (x) = - 4 x^{3} + 5 x^{2} + 8; x + 3$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Using remainder theorem.

Step 3. Using factor theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Pure Maths

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the Remainder Theorem to find the remainder when f(x)is divided by x-c. Then use the Factor Theorem to determine whether x-cis a factor of f(x). f(x)=-4x3+5x2+8;x+3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Using remainder theorem.

Step 3. Using factor theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Pure Maths

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the Remainder Theorem to find the remainder when $f (x)$ is divided by $x - c$ . Then use the Factor Theorem to determine whether $x - c$ is a factor of $f (x)$ .
$f (x) = - 4 x^{3} + 5 x^{2} + 8; x + 3$