Question 1

Which of the following best describes the zero-factor property used to solve quadratic equations?

Accepted Answer

If $$ab = 0$$, then $$a = 0 or$$ $$b = 0.$$

Question 2

Simplify the expression: $$2x^3y^2$ \cdot 3x^2$y^4.$$

Accepted Answer

$$6x^5y^6$

Question 3

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

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

Question 4

A rectangular garden has a length that is 3 meters more than twice its width. If the width is $$w$$ meters, which expression represents the area of the garden?

Accepted Answer

$$2w^2 + 3w$

Question 5

Simplify the rational expression: $$\frac{x^2$ - 4}{x + 2}.$$

Accepted Answer

$$x - 2$$

Question 6

Which of the following is the correct solution to the equation $$2x^2 - 8 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 7

Evaluate the function $$f(x) = 3x^2$ - 2x + 5$$ for $$x = -1.$$

Accepted Answer

$$10$$

Question 8

Which of the following is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 9

Simplify the radical expression: $$\sqrt{50}.$$

Accepted Answer

$$5\sqrt{2}$$

Question 10

A chemist mixes a solution with a concentration of $$x$$ grams per liter. If the total amount of solution is $$3x + 2$$ liters, which expression represents the total grams of solute?

Accepted Answer

$$x(3x + 2)$$

Question 11

Which of the following is the correct simplification of $$\frac{2x^2$y}{4xy^2$}$$?

Accepted Answer

$$\frac{x}{2y}$$

Question 12

Solve for $$x$$: $$x^2 + 6x + 9 = 0$.

Accepted Answer

$$x = -3$$

Question 13

Which of the following is a correct application of the laws of exponents: $$(x^3)^2$?

Accepted Answer

$$x^6$$

Question 14

A student is analyzing the function $$f(x) = x^2$ - 4x + 3. $$What are the zeros of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 15

Which of the following is the correct simplification of $$\sqrt{18x^2$}$$?

Accepted Answer

$$3x\sqrt{2}$$

Question 16

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial amount is $$P_0$$, which expression represents the amount after $$t$$ hours?

Accepted Answer

$$P_0$$ \cdot 2^t$$

Question 17

Which of the following is the correct solution to the equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 18

Simplify the expression: $$\frac{3}{x} + \frac{2}{x}.$$

Accepted Answer

$$\frac{5}{x}$$

Question 19

Which of the following is the correct simplification of $$\frac{x^2$ - 16}{x - 4}$$?

Accepted Answer

$$x + 4$$

Question 20

A company’s profit $$P (in $$dollars) from selling $$x$$ units is given by $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit?

Accepted Answer

$$300$$

Intermediate College Algebra Syllabus and Course Overview

Guida di studio - Domande di pratica

Study guide - Flashcard