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 multiplicity of the zero $x = -2$ for $f(x) = x^3 + 5x^2 - 2x - 10$?

Accepted Answer

Multiplicity 1

Question 5

After factoring $f(x) = x^3 + 5x^2 - 2x - 10$, which of the following is a complete factorization over the real numbers?

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

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

Question 7

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

Accepted Answer

$\left\{ -2, \dfrac{-3 + \sqrt{29}}{2}, \dfrac{-3 - \sqrt{29}}{2} \right\}$

Question 8

Which theorem is most useful for finding a possible rational zero of $f(x) = x^3 + 5x^2 - 2x - 10$?

Accepted Answer

Rational Root Theorem

Question 9

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 10

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

Accepted Answer

$f(x) 	o \infty$

Question 11

Which of the following is the remainder when $f(x) = x^3 + 5x^2 - 2x - 10$ is divided by $x - 1$?

Accepted Answer

$-6$

Question 12

If $f(x) = x^3 + 5x^2 - 2x - 10$, which of the following is the value of $f(-1)$?

Accepted Answer

$-8$

Question 13

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

Accepted Answer

$-5$

Question 14

If $f(x) = x^3 + 5x^2 - 2x - 10$, what is the y-intercept of the graph of $f(x)$?

Accepted Answer

$(0, -10)$

Question 15

Which of the following best describes the degree and leading coefficient of $f(x) = x^3 + 5x^2 - 2x - 10$?

Accepted Answer

Degree 3, leading coefficient 1

Zeros of Polynomial Functions: College Algebra Study Notes

Study Guide - Practice Questions