Question 1

Solve the equation $$2x^2 = -24x - 64$ by the zero-factor property. What is the solution set?

Accepted Answer

$$\{-4,\ 8\}$$

Question 2

Simplify $$\frac{1}{i$$^{27}$$}. $$What is the result?

Accepted Answer

$$i$$

Question 3

Solve the formula $$A = bh$$ for $$h.$$

Accepted Answer

$$h = \frac{A}{b}$$

Question 4

Simplify $$i^{81}. $$What is the result?

Accepted Answer

$$i$$

Question 5

Decide whether the equations $$3x - 2 = 8$$ and $$-3x + 8 = -2$$ are equivalent.

Accepted Answer

Equivalent

Question 6

Solve the formula $$S = 2\pi rh + 2\pi r^2$ for h$.

Accepted Answer

$$h = \frac{S - 2\pi r^2$}{2\pi r}$$

Question 7

Write $$-\sqrt{-4} as $$the product of a real number and $$i.$$

Accepted Answer

$$-2i$$

Question 8

Find the product $$(-3 + 2i)^3$ and write the answer in standard form.

Accepted Answer

$$9 + 46i$$

Question 9

Given roots $$-2$$ and $$7$$, which quadratic equation $$x^2 + bx + c = 0$ has these solutions?

Accepted Answer

$$x^2 + 5x - 14 = 0$

Question 10

Use the quadratic formula to solve $$y^2 - 14y = -32$. What is the solution set?

Accepted Answer

$$\{7 + \sqrt{17},\ 7 - \sqrt{17}\}$$

Question 11

Find the sum $$(4 - 6i) + (6 + 4i)$$ and write the answer in standard form.

Accepted Answer

$$10 - 2i$$

Question 12

Solve the equation $$x^2 + 4x + 40 = 0$ by completing the square.

Accepted Answer

$$\{-2 \pm 6i\}$$

Question 13

Solve the equation $$x^2 + 14x + 40 = 0$ by the zero-factor property.

Accepted Answer

$$\{-10, -4\}$$

Question 14

Divide $$\frac{2 + 4i}{1 + i}$$ and write the answer in the form $$a + bi.$$

Accepted Answer

$$3 + i$$

Question 15

Decide whether the statement is true or false: $$-14 is a $$solution of $$2x = -28.$$

Accepted Answer

True

Question 16

Decide whether the equation $$12(x + 3) = 2(6x + 3) + 30 is an $$identity, a conditional equation, or a contradiction. Give the solution set.

Accepted Answer

Identity: (all real numbers)

Question 17

Decide whether the equation $$5(2x - 31) = 10x - 155 is an $$identity, a conditional equation, or a contradiction. Give the solution set.

Accepted Answer

Conditional: $$\{0\}$$

Question 18

Find the sum $$(2 - 5i) + (5 + 9i)$$ and write the answer in standard form.

Accepted Answer

$$7 + 4i$$

Question 19

Solve the equation $$-6x + 1.2 = -56.4 - 1.2x. $$What is the solution?

Accepted Answer

$$\{12\}$$

Question 20

Find the product $$(8 - 3i)(7 - 5i)$$ and write the answer in standard form.

Accepted Answer

$$41 - 61i$$

College Algebra Study Guide: Quadratics, Complex Numbers, and Equations

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