Chapter 8: Q 42. (page 918)

In the following exercises, simplify.
$\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6}$

Short Answer

Expert verified

The result is $\frac{p^{2} + 4}{p - 2}$ .

Step by step solution

Step 1. Given information.

Consider the given rational expression.

$\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6}$

Step 2. Calculation.

Factor the numerator and denominator and remove the common factor from the numerator and the denominator.

$\begin{array}{l} \frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} = \frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + 3 p - 2 p - 6} \\ = \frac{p^{2} (p + 3) + 4 (p + 3)}{p (p + 3) - 2 (p + 3)} \\ = \frac{(p + 3) (p^{2} + 4)}{(p + 3) (p - 2)} \\ = \frac{p^{2} + 4}{p - 2} \end{array}$

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In the following exercises, simplify.
$\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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In the following exercises, simplify.p3+3p2+4p+12p2+p-6

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6}$