Question 1

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

Accepted Answer

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

Question 2

A chemist is mixing two solutions. The concentration of the first solution is represented by the complex number $$3 + 2i$$ and the second by $$1 - 4i. $$What is the sum of the concentrations?

Accepted Answer

$$4 - 2i$$

Question 3

Which of the following is the correct factorization of the trinomial $$x^2 + 5x + 6$?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 4

Solve the quadratic equation $$x^2 - 4x - 5 = 0$ by factoring.

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 5

A medical imaging device uses the square root of negative numbers in its calculations. What is the value of $$\sqrt{-16}$$?

Accepted Answer

$$4i$$

Question 6

Which of the following is the correct solution to the quadratic equation $$2x^2 + 3x - 2 = 0$ using the quadratic formula?

Accepted Answer

$$x = \frac{1}{2} or$$ $$x = -2$$

Question 7

A biologist is studying the growth of bacteria, which doubles every hour. If the initial population is $$P_0$$, which equation best models the population after $$t$$ hours?

Accepted Answer

$$P = P_0$ \cdot 2^t$$

Question 8

Solve the equation $$|2x - 5| = 7$$ for $$x.$$

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 9

Which of the following is the result of multiplying the complex numbers $$(2 + 3i)$$ and $$(1 - 4i)$$?

Accepted Answer

$$14 - 5i$$

Question 10

A quadratic equation $$x^2 + bx + c = 0$ has roots x = 2$ and x = -3$. What are the values of b$ and c$?

Accepted Answer

$$b = 1$$, $$c = -6$$

Question 11

Solve the equation $$x^{3/2} = 8$ for x$.

Accepted Answer

$$x = 16$$

Question 12

Which of the following is the correct solution to the equation $$x^2 + 6x + 13 = 0$?

Accepted Answer

$$x = -3 + 2i or$$ $$x = -3 - 2i$$

Question 13

A company’s profit $$P (in $$thousands of dollars) is modeled by the quadratic equation $$P = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$26$$ thousand dollars

Question 14

Solve the radical equation $$\sqrt{x + 5} = 3.$$

Accepted Answer

$$x = 4$$

Question 15

Which of the following is the correct solution to the inequality $$2x - 7 \u003c 5$$?

Accepted Answer

$$x \u003c 6$$

Question 16

A physics experiment requires you to add the complex numbers $$(-2 + 5i)$$ and $$(4 - 3i). $$What is the result?

Accepted Answer

$$2 + 2i$$

Question 17

Which of the following is the correct factorization of $$6x^2 - 11x - 10$?

Accepted Answer

$$(2x + 5)(3x - 2)$$

Question 18

Solve the equation $$\frac{2x}{x - 1} = 4$$ for $$x.$$

Accepted Answer

$$x = \frac{4}{3}$$

Question 19

Which of the following is the correct interval notation for the solution to $$x \u003e -2$$?

Accepted Answer

$$(-2, \infty)$$

Question 20

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward as $$h = -5t^2$ + 20t + 2$$, where $$t is $$time in seconds. At what time does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

College Algebra Study Guide: Factoring, Complex Numbers, Quadratic Equations, and More

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