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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. 473 (page 562)

In the following exercise, divide each polynomial by the monomial
$\frac{12 x^{2} + 4 x 鈭� 3}{鈭� 4 x}$

Short Answer

Expert verified

The solution is $- 3 x - 1 + \frac{3}{4 x}$

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{12 x^{2} + 4 x 鈭� 3}{鈭� 4 x}$

02

Step 2. Separating each terms.

$\frac{12 x^{2} + 4 x 鈭� 3}{鈭� 4 x} = \frac{12 x^{2}}{- 4 x} + \frac{4 x}{- 4 x} 鈭� \frac{3}{- 4 x}$

03

Step 3. Simplify the expression.

Using quotient property, $\frac{a^{m}}{a^{n}} = a^{m - n}$

$\frac{12 x^{2}}{- 4 x} + \frac{4 x}{- 4 x} 鈭� \frac{3}{- 4 x} = \frac{12}{- 4} x^{2 - 1} + \frac{4}{- 4} x^{1 - 1} - \frac{3}{- 4 x} 鈬� - 3 x - 1 + \frac{3}{4 x}$

04

Step 4. Simplified answer.

Hence, the simplified expression is $- 3 x - 1 + \frac{3}{4 x}$ .

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