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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.327. (page 552)

For functions $f (x) = x^{3} + 2 x^{2} - 19 x + 12$ and $g (x) = x - 3$ .
Find (a) $(\frac{f}{g}) (x)$ and (b) $(\frac{f}{g}) (0)$ .

Short Answer

Expert verified

Part (a). The solution is $x^{2} + 5 x - 4$ .

Part (b). The solution is $- 4$ .

Step by step solution

01

Part (a). Step 1. Given information.

The functions $f (x) = x^{3} + 2 x^{2} - 19 x + 12$ and $g (x) = x - 3$ .

02

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

$(\frac{f}{g}) (x) = \frac{f (x)}{g (x)} 鈬� \frac{x^{3} + 2 x^{2} - 19 x + 12}{x - 3}$

03

Part (a). Step 3. Divide the polynomials.

$x - 3 \begin{matrix} x^{2} & + 5 x & - 4 \end{matrix} \begin{matrix} x^{3} & + 2 x^{2} & - 19 x & + 12 \\ x^{3} & - 3 x^{2} \end{matrix} \overset{炉}{5 x^{2} - 19 x} 5 x^{2} - 15 x \overset{炉}{- 4 x + 12} - 4 x + 12 \overset{炉}{0}$

04

Part (a). Step (4). Simplified answer.

Hence, the obtained result is $x^{2} + 5 x - 4$ .

05

Part (b). Step 1. Given information.

The functions $f (x) = x^{3} + 2 x^{2} - 19 x + 12$ and $g (x) = x - 3$ .

06

Part (b). Step 2. To find the value of fg0 by substituting the value of x=0 in fgx=x2+5x-4.

Solve it as follows:

$(\frac{f}{g}) (0) = 0^{2} + 5 (0) - 4 鈬� 0 + 0 - 4 鈬� - 4$

07

Part (b). Step 3. Simplified answer.

Hence, the simplified expression is $- 4$ .

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