Quiz about Exploring Polynomial Functions and Roots

Question 1

Perform synthetic division on the polynomial $$f(x) = 2x^3 - 3x^2 + 4x - 5$$ by $$x - 1$$ . What is the remainder?

Accepted Answer

$$-2$$

Answer

$$0$$

Answer

$$-1$$

Answer

$$1$$

Question 2

Analyze the behavior of the polynomial $$f(x) = x^3 - 3x^2 + 2x$$ . What is the end behavior as $$x o \infty$$ ?

Accepted Answer

$$y o\infty$$

Answer

$$y o-\infty$$

Answer

$$y	o0$$

Answer

$$y$$ oscillates

Question 3

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

Accepted Answer

Cam did not use a zero place holder for the x³ term.

Answer

Cam wrote the remainder incorrectly.

Answer

Cam added instead of subtracting the rows.

Answer

Cam should have used -2 as his division since the factor was x-2.

Question 4

What are the binomial factors of $$x^2+7x-18$$

(Pick 2 answers)

Accepted Answer

$$\left(x+9\right)$$

Accepted Answer

$$\left(x-2\right)$$

Answer

$$\left(x-9\right)$$

Answer

$$\left(x+2\right)$$

Question 5

Which of the following is a POSSIBLE rational root of the polynomial $$f\left(x\right)=2x^3-5x+8\ ?$$ Select ALL that apply.

Accepted Answer

2

Accepted Answer

-8

Accepted Answer

-1/2

Answer

1/4

Answer

1/8

Question 6

Solve the polynomial equation $$x^3 - 4x^2 + 5x - 2 = 0$$ .

Accepted Answer

$$x = 1, x = 2$$

Answer

$$x = 1, x = -2$$

Answer

$$x=-2,-1$$

Answer

$$x=3,-1$$

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