Question 1

Given the polynomial $$f(x) = -2x^3$ + x^2$ - 3x + 1$$, what is the end behavior of its graph?

Accepted Answer

Rises left, falls right

Question 2

Which of the following statements is TRUE about the number of $$x-$$intercepts a polynomial of degree $$n$$ can have?

Accepted Answer

It can have at most $$n$$ $$x-$$intercepts

Question 3

Consider the polynomial $$f(x) = (x-2)^2$(x+1). $$What is the multiplicity of the root $$x=2$$ and how does the graph behave at this root?

Accepted Answer

Multiplicity 2; graph touches and turns at the $$x-$$axis

Question 4

If $$f(x) = x^4$ - 2x^2$ + 1$$, what is the maximum number of $$x-$$intercepts this polynomial can have?

Accepted Answer

$$4$$

Question 5

Which of the following is the correct application of the Factor Theorem?

Accepted Answer

If $$f(a) = 0$$, then $$(x-a) is a $$factor of $$f(x)$$

Question 6

A cubic polynomial $$f(x)$$ has a negative leading coefficient. What is the end behavior of its graph?

Accepted Answer

Rises left, falls right

Question 7

Given $$f(x) = (x-1)(x+2)(x-4)$$, which of the following is NOT a root of $$f(x)$$?

Accepted Answer

$$x = 0$$

Question 8

Suppose $$f(x) = x^5$ - 3x^3$ + 2x. $$What is the degree of $$f(x)$$ and what does this tell you about the maximum number of turns the graph can make?

Accepted Answer

Degree $$5$$; maximum $$4$$ turns

Question 9

Which polynomial could have the graph shown below: rises to the left, falls to the right, and has three $$x-$$intercepts?

Accepted Answer

$$f(x) = -x^3$ + 2x^2$ - x$$

Question 10

If $$f(x) = (x-2)^3$(x+1)$$, what is the degree of $$f(x)$$ and what is the multiplicity of the root $$x=2$$?

Accepted Answer

Degree $$4$$; multiplicity $$3$$

Question 11

A polynomial $$f(x) of $$degree $$n$$ with a positive leading coefficient and even degree will have which end behavior?

Accepted Answer

Rises both left and right

Question 12

Given $$f(x) = (x-1)^2$(x+2)$$, how many $$x-$$intercepts does the graph have?

Accepted Answer

2

Question 13

If $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following is the constant term?

Accepted Answer

$$1$$

Question 14

Which of the following polynomials has a root at $$x = -3$$ with multiplicity $$2$$?

Accepted Answer

$$f(x) = (x+3)^2$(x-1)$$

Question 15

A quartic polynomial $$f(x)$$ has only two $$x-$$intercepts. Which of the following could explain this?

Accepted Answer

Two roots have multiplicity $$2$$

Question 16

Given $$f(x) = (x-2)(x+1)(x-4)$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$-8$$

Question 17

If a polynomial $$f(x)$$ has degree $$n$$ and a root $$r$$ with multiplicity $$m$$, what does the graph do at $$x = r$$?

Accepted Answer

Touches and turns at the $$x-$$axis if $$m is $$even

Question 18

Which of the following is the correct leading term for $$f(x) = -2(x-1)(x+3)^2$(x-4)$$?

Accepted Answer

$$-2x^4$$

Question 19

A polynomial $$f(x) of $$degree $$n$$ can have at most how many turns?

Accepted Answer

$$n-1$$

Question 20

If $$f(x) = (x-2)^2$(x+1)^2$$, what is the degree of $$f(x)$$ and how many $$x$-intercepts does it have?

Accepted Answer

Degree $$4$$; $$2$$ $$x-$$intercepts

D5

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