Chapter 4: Q. 13 (page 245)

In Problems 13, find the remainder R when $f (x)$ is divided by $g (x)$ . Is $g$ a factor of $f$ ?
$f (x) = x^{4} - 2 x^{3} + 15 x - 2; g (x) = x + 2$

Short Answer

Expert verified

The remainder R is $0$ .

Yes, $g (x)$ is a factor of $f (x)$

Step by step solution

Given information

$f (x) = x^{4} - 2 x^{3} + 15 x - 2; g (x) = x + 2$

Determine whether g is a factor of f

Note: When $f (x)$ is divided by a linear polynomial $g (x)$ , the remainder $R$ is equal to $f (c)$ based from the Remainder Theorem.

$c$ is a real number from $g (x) = x - c$ . In this problem, $c = - 2$ .

Substitute $- 2$ for $x$ in $f (x)$ .

$\begin{array}{rcl} f (- 2) & = & {(- 2)}^{4} - 2 {(- 2)}^{3} + 15 (- 2) - 2 \\ = & 16 + 16 - 30 - 2 \\ = & 0 \end{array}$

Since $R = 0, g (x)$ is a factor of $f (x)$ .

Write the conclusion

The remainder is $0$ .

Yes, $g (x)$ is a factor of $f (x)$ .

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 Problems 13, find the remainder R when $f (x)$ is divided by $g (x)$ . Is $g$ a factor of $f$ ?
$f (x) = x^{4} - 2 x^{3} + 15 x - 2; g (x) = x + 2$

Short Answer

Step by step solution

Given information

Determine whether g is a factor of f

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Discrete Mathematics

Decision Maths

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 13, find the remainder R when fxis divided by gx. Is ga factor of f?f(x)=x4-2x3+15x-2;g(x)=x+2

Short Answer

Step by step solution

Given information

Determine whether g is a factor of f

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Discrete Mathematics

Decision Maths

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 13, find the remainder R when $f (x)$ is divided by $g (x)$ . Is $g$ a factor of $f$ ?
$f (x) = x^{4} - 2 x^{3} + 15 x - 2; g (x) = x + 2$