Question 1

Given the function $f(x) = x^3 - 6x^2 + 11x - 6$, which of the following is NOT a root of the function?

Accepted Answer

$x = 4$

Question 2

Which of the following is the correct factorization of $x^3 - 6x^2 + 11x - 6$?

Accepted Answer

$(x - 1)(x - 2)(x - 3)$

Question 3

If $f(x) = x^3 - 6x^2 + 11x - 6$, what is $f(2)$?

Accepted Answer

$0$

Question 4

Which of the following describes the end behavior of $f(x) = x^3 - 6x^2 + 11x - 6$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o \infty$

Question 5

Using synthetic division, what is the remainder when $x^3 - 6x^2 + 11x - 6$ is divided by $x - 2$?

Accepted Answer

$0$

Question 6

Which of the following is the correct sequence of coefficients for $x^3 - 6x^2 + 11x - 6$?

Accepted Answer

$1, -6, 11, -6$

Question 7

If you perform synthetic division of $x^3 - 6x^2 + 11x - 6$ by $x = 1$, what is the resulting quotient polynomial?

Accepted Answer

$x^2 - 5x + 6$

Question 8

Which of the following is a possible rational root of $x^3 - 6x^2 + 11x - 6$ according to the Rational Root Theorem?

Accepted Answer

$x = 1$

Question 9

After factoring $x^3 - 6x^2 + 11x - 6$, which quadratic factor remains after dividing by $(x - 1)$?

Accepted Answer

$x^2 - 5x + 6$

Question 10

Which of the following is the correct solution set for $x^3 - 6x^2 + 11x - 6 = 0$?

Accepted Answer

$\{1, 2, 3\}$

Question 11

If $f(x) = x^3 - 6x^2 + 11x - 6$, which of the following statements is true?

Accepted Answer

$f(x)$ has three real roots$

Question 12

Which synthetic division setup is correct for dividing $x^3 - 6x^2 + 11x - 6$ by $x - 3$?

Accepted Answer

Use $3$ as the divisor and coefficients $1, -6, 11, -6$

Question 13

What is the remainder when $x^3 - 6x^2 + 11x - 6$ is divided by $x - 1$?

Accepted Answer

$0$

Question 14

Which of the following is the correct order of steps for factoring a cubic polynomial like $x^3 - 6x^2 + 11x - 6$?

Accepted Answer

Find rational roots, use synthetic division, factor remaining quadratic

Question 15

If $x^3 - 6x^2 + 11x - 6$ models the population (in thousands) of a city over time $x$ (in years), what does the root $x = 2$ represent?

Accepted Answer

The population is zero at year 2

Question 16

Which of the following is the correct expanded form of $(x - 1)(x - 2)(x - 3)$?

Accepted Answer

$x^3 - 6x^2 + 11x - 6$

Question 17

If you use synthetic division to divide $x^3 - 6x^2 + 11x - 6$ by $x - 2$, what are the coefficients of the quotient polynomial?

Accepted Answer

$1, -4, 3$

Question 18

Which of the following is a correct application of the Rational Root Theorem for $x^3 - 6x^2 + 11x - 6$?

Accepted Answer

Possible rational roots are $\pm1, \pm2, \pm3, \pm6$

Question 19

If $x^3 - 6x^2 + 11x - 6$ represents the profit (in thousands of dollars) for a company over $x$ years, what does the root $x = 3$ indicate?

Accepted Answer

The company breaks even in year 3

Matrix Operations and Systems of Linear Equations: Precalculus Study Notes

Study Guide - Practice Questions