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Chapter 4: Q. 2 (page 193)

Is the expression $4 x^{3} - 3.6 x^{2} - \sqrt{2}$ a polynomial? If so, what is its degree?

Short Answer

Expert verified

The solution is yes, the expression is a polynomial with degree $3$ .

Step by step solution

01

Step 1. Given information

Expression: $4 x^{3} - 3.6 x^{2} - \sqrt{2}$

02

Step 2. Calculation

A polynomial in one variable is an algebraic expression of the form $a_{n} x^{n} + a_{n - 1} x^{n - 1} + . . . . . . . + a_{0}$ .

Here the expression $4 x^{3} - 3.6 x^{2} - \sqrt{2}$ is a polynomial where $4, (3.6), \sqrt{2}$ are the coefficients, $x$ is the variable and $3$ is the degree.

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Most popular questions from this chapter

In Problems 49– 60, for each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of $| x |$

$f (x) = 3 (x - 7) {(x + 3)}^{2}$

Make up a polynomial function that has the following characteristics: crosses the $x$ -axis at $- 1$ and $4$ , touches the $x -$ axis at $0$ and $2$ , and is above the x-axis between $0$ and $2$ . Give your polynomial function to a fellow classmate and ask for a written critique

In physics, it is established that the acceleration

due to gravity, g (in meters/sec2), at a height h meters above

sea level is given by

$g (h) = \frac{3.99 \times 10^{14}}{{(6.374 \times 10^{6} + h)}^{2}}$

where $6.374 \times 10^{6}$ is the radius of Earth in meters.

(a) What is the acceleration due to gravity at sea level?

(b)

The Willis Tower in Chicago, Illinois, is 443 meters tall.

What is the acceleration due to gravity at the top of the

Willis Tower?

(c) The peak of Mount Everest is 8848 meters above sea

level. What is the acceleration due to gravity on the

peak of Mount Everest?

(d) Find the horizontal asymptote of $g (h)$ .

(e) Solve $g (h) = 0$ . How do you interpret your answer?

Find the real zeros of f. Use the real zeros to factor f.

$f (x) = x^{3} - 8 x^{2} + 17 x - 6$

Solve each inequality algebraically.

$\frac{(x - 1) (x + 1)}{x} \leq 0$

See all solutions

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