Question 1

Solve the inequality $$x + 1 \sqrt{3} \u003e 3$$ for $$x.$$

Accepted Answer

$$x \u003e 3 - \sqrt{3}$$

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 $$x \u003c 1$$ 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 $$x \u003c 1$$ 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

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