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?

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

Study Guide - Practice Questions