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Chapter 0: Problem 30

Find each product. $$\left(7 x^{3}+5\right)\left(x^{2}-2\right)$$

Short Answer

Expert verified
The product of \( (7x^3 + 5) \) and \( (x^2 - 2) \) is \(7x^5-14x^3+5x^2-10\).

Step by step solution

01

Identify the terms

First, identify all the terms in the given polynomials. The first polynomial has the terms \(7x^3\) and \(5\). The second polynomial has the terms \(x^2\) and \(-2\).
02

Multiply each term in the first polynomial with each term in the second

Now, multiply each term in the first polynomial with each term in the second polynomial. Thus, you would have the following four products: \( (7x^3) * (x^2) \), \( (7x^3) * (-2) \), \( 5 * (x^2) \), and \( 5 * (-2) \).
03

Simplify the products

Simplify each of the products. The simplified products are \(7x^5\), \(-14x^3\), \(5x^2\), and \(-10\).
04

Add the simplified products

The final step is to add all of the simplified products together. So, the answer is \(7x^5-14x^3+5x^2-10\).

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Most popular questions from this chapter

Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone plans, long-distance telephone plans, or anything of interest. Be sure to bring in all the details for each option. At a second group meeting, select the two pricing situations that are most interesting and relevant. Using each situation, write a word problem about selecting the better of the two options. The word problem should be one that can be solved using a linear inequality. The group should turn in the two problems and their solutions.

Will help you prepare for the material covered in the next section. A telephone texting plan has a monthly fee of \(\$ 20\) with a charge of \(\$ 0.05\) per text. Write an algebraic expression that models the plan's monthly cost for \(x\) text messages.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$

How is the quadratic formula derived?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. The toll to a bridge is \(\$ 3.00 .\) A three-month pass costs \(\$ 7.50\) and reduces the toll to \(\$ 0.50 .\) A six-month pass costs \(\$ 30\) and permits crossing the bridge for no additional fee. How many crossings per three-month period does it take for the three-month pass to be the best deal?
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