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

Study Guide - Practice Questions