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Chapter 0: Problem 82

Factor completely, or state that the polynomial is prime. $$y^{5}-16 y$$

Short Answer

Expert verified
The factorization of the given polynomial \(y^{5}-16y\) is \(y(y^{4} - 16)\)

Step by step solution

01

Identify the Terms

The first step is to identify the polynomial given. In this case, it is \(y^{5}-16y\). It consists of two terms, namely \(y^{5}\) and \(-16y\).
02

Identify the Common Factor

Next, it's crucial to identify if there is a common factor that both terms in the polynomial share. Looking at the terms \(y^{5}\) and \(-16y\), a shared factor is \(y\).
03

Factorization

Now that a common factor of \(y\) is identified, this can be factored out of the polynomial. Let's factor \(y\) out of each term: \(y(y^{4} - 16)\).

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. $$\text { Multiply: }\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)$$

If you are given a quadratic equation, how do you determine which method to use to solve it?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and \(88 .\) There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I can solve \(3 x+\frac{1}{5}=\frac{1}{4}\) by first subtracting \(\frac{1}{5}\) from both sides, I find it easier to begin by multiplying both sides by \(20,\) the least common denominator.

The rational expression $$\frac{130 x}{100-x}$$ describes the cost, in millions of dollars, to inoculate \(x\) percent of the population against a particular strain of flu. a. Evaluate the expression for \(x=40, x=80,\) and \(x=90\) Describe the meaning of each evaluation in terms of percentage inoculated and cost. b. For what value of \(x\) is the expression undefined? c. What happens to the cost as \(x\) approaches \(100 \% ?\) How can you interpret this observation?
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