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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.326. (page 552)

For functions $f (x) = x^{3} + x^{2} - 7 x + 2$ and $g (x) = x - 2$ .
Find (a) $(\frac{f}{g}) (x)$ and (b) $(\frac{f}{g}) (2)$ .

Short Answer

Expert verified

Part (a). The solution is $x^{2} + 3 x - 1$ .

Part (b). The solution is $9$ .

Step by step solution

01

Part (a). Step 1. Given information.

The functions $f (x) = x^{3} + x^{2} - 7 x + 2$ and $g (x) = x - 2$ .

02

Part (a). Step 2. To divide the polynomial function by substituting the fx and gx in fgx.

Divide the given polynomials.

$x - 2 \begin{matrix} x^{2} & + 3 x & - 1 \end{matrix} \begin{matrix} x^{3} & + x^{2} & - 7 x & + 2 \\ x^{3} & - 2 x^{2} \end{matrix} \overset{炉}{3 x^{2} - 7 x} 3 x^{2} - 6 x \overset{炉}{- x + 2} - x + 2 \overset{炉}{0}$

x - 2 \begin{matrix} x^{2} & + 3 x & - 1 \end{matrix} \begin{matrix} x^{3} & + x^{2} & - 7 x & + 2 \\ x^{3} & - 2 x^{2} \end{matrix} \overset{炉}{3 x^{2} - 7 x} 3 x^{2} - 6 x \overset{炉}{- x + 2} - x + 2 \overset{炉}{0}

03

Part (a). Step 3. Simplified answer.

Hence, the obtained result is $(\frac{f}{g}) (x) = x^{2} + 3 x - 1$ .

04

Part (b). Step 1. Given information.

The functions $f (x) = x^{3} + x^{2} - 7 x + 2$ and $g (x) = x - 2$ .

05

Part (b). Step 2. To find the fg2 by substituting the x=2 in fgx=x2+3x-1.

Solve it as follows:

$(\frac{f}{g}) (2) = {(2)}^{2} + 3 (2) - 1 鈬� 4 + 6 - 1 鈬� 9$

06

Part (b). Step 3. Simplified answer.

Hence, the simplified expression is $9$ .

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