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 factorization of the trinomial $$x^3$$ - $$5x^2 - 24x$?

Accepted Answer

$$x(x - 8)(x + 3)$$

Question 2

A chemical reaction rate is modeled by the polynomial $$r(t) = t^3$ - 5t^2$ - 24t. $$What is the time $$t$$ when the rate is zero?

Accepted Answer

$$t = 0,\, t = 8,\, t = -3$$

Question 3

Which statement is true about the trinomial $$x^3$$ - $$5x^2 - 24x$?

Accepted Answer

It can be factored as $$x(x - 8)(x + 3).$$

Question 4

A company models its profit with $$P(x) = x^3$ - 5x^2$ - 24x. $$For which value of $$x$$ does the company break even?

Accepted Answer

All of the above

Question 5

Given the polynomial $$x^3$$ - $$5x^2 - 24x$, which of the following is NOT a root?

Accepted Answer

$$x = 5$$

Question 6

If $$x^3$$ - $$5x^2 - 24x$ models the volume of a container as a function of x$, for which x$ is the volume zero?

Accepted Answer

$$x = 0,\, x = 8,\, x = -3$$

Question 7

Which of the following best describes the end behavior of $$f(x) = x^3$ - 5x^2$ - 24x$$?

Accepted Answer

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

Question 8

Which of the following is the correct factorization of $$x^2 - 5x - 24$?

Accepted Answer

$$(x - 8)(x + 3)$$

Question 9

A medical dosage formula is given by $$D(x) = x^3$ - 5x^2$ - 24x. If $$the dosage must be zero, which values of $$x$$ are possible?

Accepted Answer

$$x = 0,\, x = 8,\, x = -3$$

Question 10

Which of the following is a correct statement about the polynomial $$x^3$$ - $$5x^2 - 24x$?

Accepted Answer

It can be factored into three linear factors.

Question 11

If $$x^3$$ - $$5x^2 - 24x$ represents the height of a projectile at time x$, at which times does the projectile hit the ground?

Accepted Answer

$$x = 0,\, x = 8,\, x = -3$$

Question 12

Which of the following is the correct set of roots for $$x^2 - 5x - 24 = 0$?

Accepted Answer

$$x = 8,\, x = -3$$

Question 13

A polynomial $$x^3$$ - $$5x^2 - 24x$ is used to model the population of a species. If the population is zero, what are the possible values of x$?

Accepted Answer

$$x = 0,\, x = 8,\, x = -3$$

Question 14

Which of the following is the correct factorization of $$x^3$$ - $$5x^2 - 24x$?

Accepted Answer

$$x(x - 8)(x + 3)$$

Question 15

If $$x^3$$ - $$5x^2 - 24x$ models the revenue of a business, what is the significance of the roots?

Accepted Answer

They represent the values of $$x$$ where the revenue is zero.

Question 16

Which of the following is NOT a factor of $$x^3$$ - $$5x^2 - 24x$?

Accepted Answer

$$(x - 5)$$

Question 17

A polynomial $$x^3$$ - $$5x^2 - 24x$ is used to model the cost of production. If the cost is zero, what are the possible values of x$?

Accepted Answer

$$x = 0,\, x = 8,\, x = -3$$

Factoring and Primality of Polynomials: Study Notes for Precalculus

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