Chapter 4: Q. 12 (page 245)

In Problems 13, find the remainder R when $f (x)$ is divided by $g (x)$ . Is $g$ a factor of $f$ ?
$f (x) = 8 x^{3} - 3 x^{2} + x + 4; g (x) = x - 1$

Short Answer

Expert verified

The remainder R is $10$ .

No, $g (x)$ is not a factor of $f (x)$

Step by step solution

Given information

The given function is $f (x) = 8 x^{3} - 3 x^{2} + x + 4; g (x) = x - 1$

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, $c = 1$ .

Substitute $1$ for $x$ in $f (x)$ .

$\begin{array}{rcl} f (x) & = & 8 {(1)}^{3} - 3 {(1)}^{2} + (1) + 4 \\ = & 8 - 3 + 1 + 4 \\ = & 10 \end{array}$

Since, $R = 10$ , $g (x)$ is not a factor of $f (x)$

Write the conclusion

The remainder is $10$ .

No, $g (x)$ is not a factor of $f (x)$ .

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In Problems 13, find the remainder R when $f (x)$ is divided by $g (x)$ . Is $g$ a factor of $f$ ?
$f (x) = 8 x^{3} - 3 x^{2} + x + 4; g (x) = x - 1$

Short Answer

Step by step solution

Given information

Determine whether g is a factor of f

Write the conclusion

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Most popular questions from this chapter

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In Problems 13, find the remainder R when fxis divided by gx. Is ga factor of f? f(x)=8x3-3x2+x+4;g(x)=x-1

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

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Probability and Statistics

Discrete 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 $f$ ?
$f (x) = 8 x^{3} - 3 x^{2} + x + 4; g (x) = x - 1$