Q: Which of the following best describes the end behavior of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

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

Question 1

Given the function $$f(x) = x^3$ + 5x^2$ - 2x - 10$$, which of the following is a zero of the function?

Accepted Answer

$$x = -2$$

Question 2

Which of the following is a factor of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

Accepted Answer

$$x + 2$$

Question 3

If $$x = -2 is a $$zero of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$, what is the result of dividing $$f(x) by$$ $$x + 2$$?

Accepted Answer

$$x^2 + 3x - 5$

Question 4

Which of the following best describes the end behavior of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

Accepted Answer

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

Question 5

Which of the following is the correct factorization of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

Accepted Answer

$$(x + 2)(x^2$ + 3x - 5)$$

Question 6

Which of the following is a real zero of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

Accepted Answer

$$x = \frac{-3 + \sqrt{29}}{2}$$

Question 7

Which of the following methods is most appropriate to find all zeros of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

Accepted Answer

Use synthetic division to find a rational zero, then factor the resulting quadratic.

Question 8

If $$f(x) = x^3$ + 5x^2$ - 2x - 10$$ models the profit (in thousands of dollars) for a company, for which value of $$x$$ does the company break even?

Accepted Answer

$$x = -2$$

Question 9

Given $$f(x) = x^3$ + 5x^2$ - 2x - 10$$, which of the following is the correct set of all real zeros?

Accepted Answer

$$x = -2, \; x = \frac{-3 + \sqrt{29}}{2}, \; x = \frac{-3 - \sqrt{29}}{2}$$

Question 10

If $$f(x) = x^3$ + 5x^2$ - 2x - 10$$ represents the volume (in cubic meters) of a tank as a function of its length $$x (in $$meters), for which value of $$x is $$the volume zero?

Accepted Answer

$$x = -2$$

Question 11

Which of the following statements is true about the graph of $$f(x) = x^3$ + 5x^2$ - 2x - 10$$?

Accepted Answer

It has one local maximum and one local minimum.

Question 12

If $$f(x) = x^3$ + 5x^2$ - 2x - 10$$, what is $$f(-1)$$?

Accepted Answer

$$f(-1) = -1 + 5 + 2 - 10 = -4$$

Zeros of Polynomial Functions: College Algebra Review

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