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

Question 1

What is the degree of the polynomial $$p(x) = 5x(x+2)^3$(x-1)$$?

Accepted Answer

$$5$$

Question 2

Which of the following best describes the end behavior of $$g(x) = -2x^4$ + 3x^2$ - 4x + 10$$?

Accepted Answer

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

Question 3

What are the $$x-$$intercepts of $$h(x) = x(x-1)^2$(x+5)^3$?

Accepted Answer

$$x = 0, 1, -5$$

Question 4

If a third degree polynomial has a real zero at $$x=2$$ and a complex zero at $$x=3+2i$$, what is the other zero?

Accepted Answer

$$x = 3-2i$$

Question 5

A polynomial is known to have degree $$8. $$What is the maximum number of real zeros the polynomial can have?

Accepted Answer

$$8$$

Question 6

Compute and simplify $$(2 + 3i)(2 - 3i).$$

Accepted Answer

$$13$$

Question 7

Simplify $$i^6.$$

Accepted Answer

$$1$$

Question 8

What is the maximum number of turning points for $$p(x) = 2x(x+2)^3$(x-1)^2$?

Accepted Answer

$$5$$

Question 9

Given $$f(x) = -2x^3$ + 5x^2$ - 3x + 1$$, what is the $$y-$$intercept?

Accepted Answer

$$1$$

Question 10

Which of the following is NOT a polynomial?

Accepted Answer

$$f(x) = 3x^3$ + 4x^2$ - \frac{1}{x}$$

Question 11

How many possible rational zeros exist for $$p(x) = 4x^3$ + 3x^2$ - 2$$ according to the Rational Zero Theorem?

Accepted Answer

$$12$$

Question 12

Which of the following is the standard form of a degree 3 polynomial with zeros at $$x=2$$, $$x=1$$, and $$x=-1$$, and leading coefficient $$1$$?

Accepted Answer

$$x^3$$ - $$2x^2 - x + 2$

Question 13

If $$x-2 is a $$factor of $$p(x) = x^3$ - 2x^2$ + 3x - 6$$, what is $$p(2)$$?

Accepted Answer

$$0$$

Question 14

Given $$f(x) = x^3$ - 8x^2$ + 25x - 26$$, which of the following is a complex zero?

Accepted Answer

$$x = 4 + i$$

Question 15

Which of the following describes the domain of any polynomial function?

Accepted Answer

$$(-\infty, \infty)$$

Question 16

If a polynomial $$p(x)$$ has a zero at $$x = a$$ with multiplicity $$3$$, what is the behavior of the graph at $$x = a$$?

Accepted Answer

The graph crosses the $$x-$$axis and flattens (wiggles) at $$x = a$$

Question 17

Which of the following is a possible rational zero of $$p(x) = x^3$ + 4x^2$ + x - 6$$?

Accepted Answer

$$-1$$

Question 18

Given $$p(x) = 2x(x+2)^3$(x-1)^2$$, what is the $$y$-intercept?

Accepted Answer

$$0$$

Question 19

Which of the following best describes the range of a cubic polynomial with a negative leading coefficient?

Accepted Answer

$$(-\infty, \infty)$$

Precalculus Polynomial Review: Step-by-Step Guidance

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