$(-\infty, 1) \cup [2, \infty)$

$2(x - 2)(x^4 + 2x^3 + 4x^2 + 8x + 16)$

$(-\infty, 1) \cup [2, \infty)$

Question 1

Solve the inequality $x + 1 \sqrt{3} > 3$ for $x$.

Accepted Answer

$x > 3 - \sqrt{3}$

Question 2

Given $f(x) = x^2 - 4x + 8$, find the vertex of the parabola.

Accepted Answer

$(2, 4)$

Question 3

Rewrite $f(x) = x^2 + 12x + 33$ in vertex form $a(x-h)^2 + k$.

Accepted Answer

$f(x) = (x + 6)^2 - 3$

Question 4

Find the exact value of $\sqrt{18}$.

Accepted Answer

$3\sqrt{2}$

Question 5

Simplify $(3 + i)(4 - i)$.

Accepted Answer

$13 + i$

Question 6

Divide $\frac{2 + i}{3 - 2i}$ and write your answer in the form $a + bi$.

Accepted Answer

$\frac{4}{13} + \frac{7}{13}i$

Question 7

Which of the following is the correct factorization of $x^2 - 64$?

Accepted Answer

$(x - 8)(x + 8)$

Question 8

Determine the zeros of the function $x^2 + 4x - 5$ by factoring.

Accepted Answer

$x = 1, x = -5$

Question 9

Given $f(x) = x^4 + 4x$, and $x = 0$ is a zero, find all remaining zeros.

Accepted Answer

$x = 0, x = 0, x = 2i, x = -2i$

Question 10

What is the degree of the polynomial $2x^6 + x - 12 = 0$?

Accepted Answer

$6$

Question 11

If $f(x) = 3x + 2$ for $x < 1$ and $f(x) = x - 5$ for $x \geq 2$, what is the domain of $f(x)$?

Accepted Answer

$(-\infty, 1) \cup [2, \infty)$

Question 12

Which of the following is the correct factorization of $2x^5 - 32$?

Accepted Answer

$2(x - 2)(x^4 + 2x^3 + 4x^2 + 8x + 16)$

Question 13

Given $f(x) = x^2 - 10x + 11$, fully factor the polynomial.

Accepted Answer

$(x - 1)(x - 11)$

Question 14

Divide $3x^2 - 2x + 1$ by $x - 1$ using synthetic division. What is the remainder?

Accepted Answer

$2$

Question 15

What is the end behavior of $g(x) = x^4 + 4x$ as $x 	o \infty$?

Accepted Answer

$g(x) 	o \infty$

Question 16

Which interval(s) is the function $f(x)$ continuous if $f(x)$ is defined as $f(x) = 3x + 2$ for $x < 1$ and $f(x) = x - 5$ for $x \geq 2$?

Accepted Answer

$(-\infty, 1) \cup [2, \infty)$

Question 17

If $f(x) = x^2 + 4x = -4$, what is the value of $x$?

Accepted Answer

$x = -2 \pm 2\sqrt{2}$

Question 18

Which of the following describes the end behavior of $f(x) = -3x^2 + 2x - 1$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o -\infty$

Question 19

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

Accepted Answer

$-4$

College Algebra: Functions, Polynomials, and Quadratics Study Guide

Study Guide - Practice Questions