Question 1

Given the polynomial $$P(x) = 2x^3$ + 9x^2$ + 6x - 8$$, which of the following lists all possible rational zeros according to the Rational Root Theorem?

Accepted Answer

$$\pm 1, \pm \frac{1}{2}, \pm 2, \pm 4, \pm 8$$

Question 2

Which of the following is the correct application of the Rational Root Theorem for the polynomial $$f(x) = 3x^4$ - 5x^3$ + 2x - 6$$?

Accepted Answer

Possible rational zeros are $$\pm 1, \pm 2, \pm 3, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{1}{6}, \pm \frac{2}{6}$$

Question 3

A chemical reaction is modeled by the polynomial $$C(t) = t^3$ - 4t^2$ + t + 6. $$Which of the following is a possible rational zero?

Accepted Answer

$$-2$$

Question 4

If $$P(x) = 4x^3$ - 7x^2$ + 2x - 8$$, which of the following is NOT a possible rational zero?

Accepted Answer

$$\frac{7}{4}$$

Question 5

A population model is given by $$P(x) = x^3$ - 2x^2$ - 5x + 6. $$Which of the following is a rational zero of $$P(x)$$?

Accepted Answer

$$2$$

Question 6

Given $$f(x) = 2x^3$ - 3x^2$ + 4x - 6$$, which of the following is a possible rational zero?

Accepted Answer

$$\frac{1}{2}$$

Question 7

A polynomial $$Q(x) = 5x^3$ + 10x^2$ - 15x + 20$$ models the profit of a business. Which of the following is NOT a possible rational zero?

Accepted Answer

$$\frac{3}{5}$$

Question 8

Which of the following best describes the Rational Root Theorem?

Accepted Answer

It provides a list of all possible rational roots based on the factors of the leading coefficient and the constant term.

Question 9

A medical dosage model is given by $$D(x) = x^3$ + 2x^2$ - 5x - 6. $$Which of the following is a possible rational zero?

Accepted Answer

$$3$$

Question 10

Given the polynomial $$R(x) = 6x^3$ - 5x^2$ + 4x - 2$$, which of the following is a possible rational zero?

Accepted Answer

$$\frac{1}{2}$$

Question 11

A polynomial $$S(x) = x^4$ - 3x^3$ + 2x^2$ - x + 2 is $$used to model a physics experiment. Which of the following is NOT a possible rational zero?

Accepted Answer

$$\frac{3}{2}$$

Question 12

If $$T(x) = 3x^3$ + 2x^2$ - x + 4$$, which of the following is a possible rational zero?

Accepted Answer

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

Question 13

A polynomial $$U(x) = 2x^3$ - 4x^2$ + 6x - 8 is $$used in an engineering context. Which of the following is a possible rational zero?

Accepted Answer

$$\frac{2}{1}$$

Question 14

Given $$V(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a possible rational zero?

Accepted Answer

$$4$$

Question 15

A polynomial $$W(x) = 4x^3$ + 8x^2$ - 12x + 16 is $$used to model a chemical process. Which of the following is a possible rational zero?

Accepted Answer

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

Rational Zeros of Polynomials: Practice Test Review

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