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

Question 1

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

Accepted Answer

$$4x^5$$ - $$3x^3$$ + $$x^2$$

Question 2

What is the degree and leading coefficient of the polynomial $$f(x) = 7x^4$ - 2x^2$ + 5$$?

Accepted Answer

Degree: 4, Leading Coefficient: 7

Question 3

Which of the following is a quadratic trinomial?

Accepted Answer

$$x^2 + 3x + 2$

Question 4

Given $$f(x) = x^3$ - 2x^2$ + x - 5$$ and $$g(x) = 2x^2$ - x + 3$$, what is $$f(x) + g(x) in $$standard form?

Accepted Answer

Question 5

Multiply $$(2x - 3)(x^2$ + x + 1)$$ and write the answer in standard form.

Accepted Answer

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

Question 6

Which of the following is the factored form of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 7

If $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, use synthetic division to divide $$f(x) by$$ $$x - 2. $$What is the remainder?

Accepted Answer

4

Question 8

According to the Fundamental Theorem of Algebra, how many solutions does a polynomial equation of degree 5 have?

Accepted Answer

5

Question 9

Which of the following is a possible rational zero of $$f(x) = 2x^3$ - 3x^2$ + x - 6$$ according to the Rational Zero Theorem?

Accepted Answer

$$\frac{1}{2}$$

Question 10

What is the end behavior of $$f(x) = -2x^4$ + 5x^2$ - 1 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 11

If a polynomial function has a zero at $$x = 2$$ with multiplicity 3, what happens to the graph at $$x = 2$$?

Accepted Answer

The graph crosses the x-axis at $$x = 2$$

Question 12

Expand $$(x + 2)^3$ using Pascal's Triangle.

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 13

Which of the following is the correct factorization for $$8x^3 - 27$?

Accepted Answer

$$(2x - 3)(4x^2$ + 6x + 9)$$

Question 14

Given $$f(x) = x^4$ - 5x^2$ + 4$$, which of the following is a correct complete factorization over the real numbers?

Accepted Answer

$$(x^2$$ - $$4)(x^2 - 1$$)$$

Question 15

Divide $$2x^3$$ + $$4x^2 + 10$ by x + 2$ using synthetic division. What is the quotient?

Accepted Answer

$$2x^2 + 0x + 10$

Question 16

A polynomial function $$f(x)$$ has degree 6. What is the maximum number of turning points it can have?

Accepted Answer

5

Question 17

Which of the following is NOT a polynomial?

Accepted Answer

$$x^{-1} + 2$

Question 18

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is a zero of $$f(x)$$?

Accepted Answer

1

Question 19

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

Accepted Answer

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

Unit 2 Study Guide

스터디 가이드 - 연습 문제