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

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