As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Which of the following is a polynomial of degree 3?

Accepted Answer

$$x^3 - 2x + 4$

Question 2

Given the polynomial $$f(x) = 3x^4$ - 2x^2$ + x - 5$$, what is the leading coefficient?

Accepted Answer

$$3$$

Question 3

Which of the following is NOT a polynomial?

Accepted Answer

$$x^2$$ + \sqrt{x}$$

Question 4

What is the minimum degree a polynomial can have if its graph has 3 turning points?

Accepted Answer

$$4$$

Question 5

If a polynomial has a zero at $$x = 2$$ with multiplicity 3, what does the graph do at $$x = 2$$?

Accepted Answer

It crosses the x-axis and turns around.

Question 6

Which of the following describes the end behavior of $$f(x) = -2x^5$ + x^3$ - 4$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 7

Which of the following is the standard form of a polynomial?

Accepted Answer

$$a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$

Question 8

A polynomial $$f(x)$$ has zeros at $$x = -3, 0, 2$$ with multiplicities 1, 2, and 1 respectively. What is the minimum degree of $$f(x)$$?

Accepted Answer

$$4$$

Question 9

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 10

If $$f(x) = x(x+2)^2$(x-1)$$, what is the multiplicity of the zero at $$x = 2$$?

Accepted Answer

$$2$$

Question 11

Which graph represents a polynomial with an odd degree and a positive leading coefficient?

Accepted Answer

Graph B

Question 12

What is the degree of the polynomial $$f(x) = 7x^6$ - 3x^4$ + 2x^2$ - 1$$?

Accepted Answer

$$6$$

Question 13

If a polynomial has a constant term only, what is its degree?

Accepted Answer

$$0$$

Question 14

Which of the following is a linear polynomial?

Accepted Answer

$$3x + 4$$

Question 15

Given $$f(x) = x^2$(x-1)^3(x+2$$)$, what is the total number of real zeros (counting multiplicity)?

Accepted Answer

$$5$$

Question 16

Which property is true for zeros of even multiplicity?

Accepted Answer

The graph touches the x-axis and turns around.

Question 17

If $$f(x) = x^3$ - 4x^2$ + x - 6$$, what is the sum of the coefficients?

Accepted Answer

Question 18

Which of the following is the correct classification for $$-7x + 2$$?

Accepted Answer

Linear

Question 19

If a polynomial has degree $$n$$, what is the maximum number of turning points it can have?

Accepted Answer

$$n-1$$

Question 20

Which of the following is a term in the polynomial $$f(x) = 4x^3$ - 2x^2$ + x - 5$$?

Accepted Answer

$$4x^3$$

Polynomials: Structure, Classification, and Graphical Behavior

Study Guide - Practice Questions