Question 1

Which of the following is the correct general form of a polynomial equation of degree $$n$$?

Accepted Answer

$$a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$ = 0$$

Question 2

Solve the equation $$x^2 - 8x + 12 = 0$ by factoring.

Accepted Answer

$$x = 2 or$$ $$x = 6$$

Question 3

Which step is NOT part of the process for solving radical equations containing nth roots?

Accepted Answer

Multiply both sides by the nth root.

Question 4

Solve the radical equation $$\sqrt{x+3} = x - 1. $$Which value is a valid solution?

Accepted Answer

$$x = 4$$

Question 5

Which of the following is equivalent to the equation $$x^{\frac{2}$${3}} = 8$$?

Accepted Answer

$$(x^{\frac{1}$${3}}$$)^2 = 8$

Question 6

Solve the equation $$x^{\frac{2}$${3}} = 8$$. What is the value of x$?

Accepted Answer

$$x = 64$$

Question 7

Which equation is quadratic in form?

Accepted Answer

$$x^4$$ - $$5x^2 + 6 = 0$

Question 8

Solve the equation $$x^4$$ - $$5x^2 + 6 = 0$ by substitution.

Accepted Answer

$$x = \pm \sqrt{2} or$$ $$x = \pm \sqrt{3}$$

Question 9

Which of the following is the correct interpretation of $$|u| = c$$ for $$c \u003e 0$$?

Accepted Answer

$$u = c or$$ $$u = -c$$

Question 10

Solve the absolute value equation $$|2x - 5| = 1.$$

Accepted Answer

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

Question 11

A chemical reaction's rate is modeled by $$R = k \sqrt{C}$$, where $$C is $$concentration. If $$R = 10$$ and $$k = 2$$, what is $$C$$?

Accepted Answer

$$C = 25$$

Question 12

The formula $$H = -2.3I + 67.6$$ models weekly TV viewing hours $$H by $$annual income $$I (in $$thousands). What is the annual income for $$H = 33.1$$?

Accepted Answer

$$I = 15$$

Question 13

Which of the following is a necessary step when solving a radical equation such as $$\sqrt{x+2} = x$$?

Accepted Answer

Raise both sides to the second power to eliminate the radical.

Question 14

Solve the equation $$x^3$$ + $$3x^2 + 2x = 0$ by factoring.

Accepted Answer

$$x = 0$$, $$x = -1$$, $$x = -2$$

Question 15

A medical dosage formula is $$D = \sqrt{W}$$, where $$D is $$dosage and $$W is $$weight. If a patient needs a dosage of $$D = 7$$, what is their weight?

Accepted Answer

$$W = 49$$

Question 16

Which equation is NOT quadratic in form?

Accepted Answer

$$x^3$$ + $$2x^2 + x = 0$

Question 17

Solve the equation $$x^2 - 5x + 6 = 0$ by factoring.

Accepted Answer

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

Question 18

If $$|u| = c$$ and $$c is $$negative, what is the solution?

Accepted Answer

No solution exists.

Question 19

A population model is $$P = \sqrt{A}$$, where $$A is $$area. If $$P = 10$$, what is $$A$$?

Accepted Answer

$$A = 100$$

Other Types of Equations: Polynomial, Radical, Rational Exponents, Quadratic Form, and Absolute Value

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