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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