Question 1

Given the polynomial $$f(x) = -2x^4$ + 3x^3$ - x + 5$$, what is the end behavior of the graph?

Accepted Answer

Rises to the left and falls to the right

Question 2

Which of the following statements is TRUE about the number of $$x-$$intercepts a degree 5 polynomial can have?

Accepted Answer

It can have up to 5 $$x-$$intercepts, but possibly fewer

Question 3

Consider the polynomial $$f(x) = (x+2)^2$(x-1). $$Which statement best describes the behavior of the graph at $$x = -2$$?

Accepted Answer

The graph touches the $$x-$$axis and turns around at $$x = -2$$

Question 4

A cubic polynomial $$f(x)$$ has a positive leading coefficient. Which of the following best describes its end behavior?

Accepted Answer

Falls to the left and rises to the right

Question 5

If $$f(x) = x^3$ - 4x^2$ + x$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$y = 0$$

Question 6

Which of the following polynomials could have exactly 2 $$x-$$intercepts?

Accepted Answer

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

Question 7

A degree 4 polynomial has a negative leading coefficient. Which of the following describes its end behavior?

Accepted Answer

Both ends fall

Question 8

Given $$f(x) = (x-2)^3$(x+1)$$, what is the multiplicity of the root at $$x = 2$$ and how does the graph behave there?

Accepted Answer

Multiplicity 3; graph crosses and flattens at the axis

Question 9

If $$f(x) = x^4$ - 5x^2$ + 4$$, what is the maximum number of turning points the graph can have?

Accepted Answer

3

Question 10

Which of the following is a possible graph for a degree 3 polynomial with a negative leading coefficient?

Accepted Answer

Rises to the left and falls to the right

Question 11

A polynomial $$f(x)$$ has roots at $$x = -1 ($$multiplicity 2), $$x = 0 ($$multiplicity 1), and $$x = 3 ($$multiplicity 1). What is the degree of $$f(x)$$?

Accepted Answer

4

Question 12

If $$f(x) = -x^2$(x-1)$$, which of the following best describes the $$y-$$intercept?

Accepted Answer

$$y = 0$$

Question 13

Which of the following is TRUE about the number of turning points of a degree $$n$$ polynomial?

Accepted Answer

It can have at most $$n-1$$ turning points

Question 14

Given $$f(x) = (x+1)^2$(x-2)$$, what is the degree and leading coefficient of $$f(x)$$?

Accepted Answer

Degree 3, leading coefficient 1

Question 15

If $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following could be a factor of $$f(x)$$?

Accepted Answer

$$x^2 - 1$

Question 16

A degree 6 polynomial has a positive leading coefficient. Which statement is correct about its end behavior?

Accepted Answer

Both ends rise

Question 17

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

Accepted Answer

2

Question 18

Which of the following is NOT a possible number of $$x-$$intercepts for a degree 4 polynomial?

Accepted Answer

3

Question 19

Given $$f(x) = -2(x+1)^3$(x-2)$$, what is the degree and leading coefficient?

Accepted Answer

Degree 4, leading coefficient -2

Question 20

A real-world scenario: The height $$h(t) (in $$meters) of a projectile is modeled by $$h(t) = -5t^2$ + 20t + 1. $$What is the degree of this polynomial and what does it tell you about the graph's shape?

Accepted Answer

Degree 2; the graph is a parabola opening downward

D5

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