As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following is the correct standard form of the equation $$x^3 - 8x + 1 = 0$?

Accepted Answer

$$x^3 - 8x + 1 = 0$

Question 2

What is the degree of the polynomial $$x^3 - 8x + 1$?

Accepted Answer

3

Question 3

Which of the following describes the end behavior of the function $$f(x) = x^3$ - 8x + 1$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 4

Which of the following is the correct rearrangement of $$2 - \frac{4}{3}x^2$ = x^3$ - \frac{5}{2}x to $$standard form?

Accepted Answer

$$x^3$$ + \frac{4}{3}$$x^2$$ - \frac{5}{2}x - 2 = 0$$

Question 5

If you use a graphing utility to approximate the real solutions of $$x^3 - 8x + 1 = 0$, what are you finding?

Accepted Answer

The $$x-$$intercepts of the graph of $$y = x^3$ - 8x + 1$$

Question 6

Which of the following is a possible rational root of $$x^3 - 8x + 1 = 0$ according to the Rational Root Theorem?

Accepted Answer

$$1$$

Question 7

What is the coefficient of $$x^2 in $$the equation $$2 - \frac{4}{3}x^2$ = x^3$ - \frac{5}{2}x$$ when written in standard form?

Accepted Answer

$$\frac{4}{3}$$

Question 8

Which of the following best describes the number of real solutions a cubic equation can have?

Accepted Answer

One or three real solutions

Question 9

Suppose you are modeling the height of a projectile with $$h(t) = t^3$ - 8t + 1. $$What does solving $$t^3 - 8t + 1 = 0$ represent in this context?

Accepted Answer

Finding the time(s) when the projectile hits the ground

Question 10

Which of the following is the correct first step to solve $$2 - \frac{4}{3}x^2$ = x^3$ - \frac{5}{2}x$$ for $$x$$?

Accepted Answer

Move all terms to one side to set the equation equal to zero

Solving Cubic Equations and Polynomial Equations in College Algebra

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