Question 1

Which of the following is a correct definition of a polynomial?

Accepted Answer

A combination of numbers and variables with only nonnegative integer exponents and no variables in the denominator.

Question 2

Simplify the expression $$3x + 2x - 5y.$$

Accepted Answer

$$5x - 5y$$

Question 3

What is the degree and classification of the polynomial $$4x^2 - 5x + 3$?

Accepted Answer

Degree 2, trinomial

Question 4

Which of the following pairs are similar terms?

Accepted Answer

$$8b$$ and $$81b$$

Question 5

Simplify the expression $$2(a + 2x) - (a - 3c).$$

Accepted Answer

$$a + 4x + 3c$$

Question 6

Multiply the monomials: $$3c^5(-4c^2$)$.

Accepted Answer

$$-12c^7$$

Question 7

Find the product: $$(x - 2)(x + 3).$$

Accepted Answer

$$x^2 + x - 6$

Question 8

Divide the following: $$\frac{16x^3$y^5$$}{$$4xy^2$$}$.

Accepted Answer

$$4x^2y^3$

Question 9

Using long division, what is the quotient and remainder when $$6x^2 + x - 2$ is divided by 2x - 1$?

Accepted Answer

$$3x + 2 + \frac{0}{2x - 1}$$

Question 10

Solve for $$x$$: $$x - 7 = 3x - (6x - 8).$$

Accepted Answer

$$x = 1$$

Question 11

Which of the following is a conditional equation?

Accepted Answer

$$x^2 - 4 = (x - 2)(x + 2$$)$$

Question 12

Set up and solve the proportion: The ratio of $$x to$$ $$8$$ equals $$3 to$$ $$4. $$What is $$x$$?

Accepted Answer

$$x = 6$$

Question 13

Which property of inequalities explains why multiplying both sides of $$a \u003e b by$$ $$-1$$ reverses the inequality?

Accepted Answer

Multiplying both sides by a negative number reverses the inequality.

Question 14

Solve the inequality: $$3 - 2x \geq 15.$$

Accepted Answer

$$x \leq -6$$

Question 15

Solve the three-member inequality: $$-1 \u003c 2x + 3 \u003c 6.$$

Accepted Answer

$$-2 \u003c x \u003c 1.5$$

Question 16

Which of the following is an absolute inequality?

Accepted Answer

$$x^2$$ \geq 0$$ for all real x$

Question 17

A chemist needs to dilute a solution. The ratio of solute to solvent must be $$1:4. If $$the chemist has $$20 mL of $$solute, how much solvent is needed?

Accepted Answer

$$80 mL$$

Question 18

Which of the following is the correct simplification of $$y(3 - y) - 2(y - 3)$$?

Accepted Answer

$$-y^2 + 5y - 6$

Question 19

A company’s profit $$P is $$given by $$P = 2x - 500$$, where $$x is $$the number of units sold. What is the minimum number of units that must be sold for the profit to be at least zero?

Accepted Answer

$$x \geq 250$$

Algebraic Expressions, Linear Equations, and Inequalities: Precalculus Study Guide

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