Algebraic Expressions: Master the Basics for College Algebra

Question 1

Identify the expression that is NOT an algebraic expression:

Accepted Answer

10

Answer

2x + 5

Answer

(x - 3)(x + 2)

Answer

-5y^2

Question 2

Expand the expression: (x - 2)^2

Accepted Answer

x^2 - 4x + 4

Answer

x^2 - 4

Answer

x^2 + 4

Answer

x^2 - 8x + 4

Question 3

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 3)(x + 3)

Answer

(x - 3)(x - 3)

Question 4

Solve for x: 2x - 5 = 15

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 5

Which of the following is a constant?

Accepted Answer

2

Answer

x

Answer

y + 3

Answer

x^2

Question 6

Distribute and simplify the expression: 3(x + 2) - 2x

Accepted Answer

5x + 6

Answer

x + 6

Answer

x - 2

Answer

5x - 2

Question 7

Substitute the values x = 2 and y = 1 into the expression: 2x^2 - 3y

Accepted Answer

11

Answer

5

Answer

15

Answer

21

Question 8

Combine like terms and simplify the expression: 2(3x - 4) + 5x

Accepted Answer

11x - 8

Answer

7x - 8

Answer

11x + 8

Answer

7x + 8

Question 9

Identify the constant term in the expression: 5x^2 - 2x + 3

Accepted Answer

3

Answer

5

Answer

-2

Answer

0

Question 10

Which of the following operations is NOT used during the simplification of algebraic expressions?

Accepted Answer

Division

Answer

Addition

Answer

Multiplication

Answer

Subtraction

Question 11

Solve the equation for x: 3x - 5 = 10

Accepted Answer

7

Answer

5

Answer

15

Answer

17

Question 12

Identify the quadratic expression:

Accepted Answer

x^2 - 5x + 3

Answer

3x + 2

Answer

2x - 1

Answer

5x^3 - 2x^2 + x

Question 13

Expand the square expression: (x + 2)^2

Accepted Answer

x^2 + 4x + 4

Answer

x^2 + 4

Answer

x^2 - 4x + 4

Answer

x^2 - 4

Question 14

Evaluate the algebraic expression 2(x - 3) + 4 when x is assigned a value of 5.

Accepted Answer

16

Answer

2

Answer

12

Answer

20

Question 15

Which algebraic expression is equivalent to 3(2x - 1)?

Accepted Answer

6x - 3

Answer

6x + 3

Answer

2x - 3

Answer

2x + 3

Question 16

Evaluate the algebraic expression: sqrt(16) + abs(-5)

Accepted Answer

11

Answer

1

Answer

5

Answer

9

Question 17

Which term in the algebraic expression 3x^2 - 2x + 5 is NOT a constant?

Accepted Answer

x

Answer

3

Answer

-2

Answer

5

Question 18

Simplify the algebraic expression: (2x - 3)^2

Accepted Answer

4x^2 + 12x - 9

Answer

4x^2 - 9

Answer

4x^2 - 6x + 9

Answer

4x^2 + 6x + 9

Question 19

Which algebraic expression is equivalent to x^2 + 2xy + y^2?

Accepted Answer

(x + y)^2

Answer

(x - y)^2

Answer

(2x + y)^2

Answer

(x^2 + y^2)^2

Question 20

In the algebraic expression 2x - 5, what does the letter x represent?

Accepted Answer

An unknown number

Answer

A specific number

Answer

An operation like addition or subtraction

Answer

A real number like 1 or 2

Question 21

In the algebraic expression 2x - 5, what does the -5 represent?

Accepted Answer

A constant value

Answer

A variable value

Answer

A numeric expression

Answer

An operational symbol

Question 22

Simplify the following expression: (2x^(2/5) + 3y^(1/3))^(5/2)

Accepted Answer

4x^(5/2) + 12y^(5/6)

Answer

8x + 24y

Answer

10x^(2/5) + 15y^(1/3)

Answer

2x^5 + 3y^5

Question 23

Determine the algebraic expression for the line passing through points (2, 5) and (4, 9). Sketch the line's graph.

Accepted Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = 2x - 1

Answer

y = 3x + 1

Question 24

Which operation is NOT applicable to algebraic expressions?

Accepted Answer

Differentiating

Answer

Adding

Answer

Subtracting

Answer

Multiplying

Question 25

Which operation is NOT typically performed directly on algebraic expressions?

Accepted Answer

Differentiation

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 26

Which of the following is an example of a variable in an algebraic expression?

Accepted Answer

x

Answer

+

Answer

y = 3

Answer

2

Question 27

Simplify the expression: 3x + 2y - x + 4y

Accepted Answer

2x + 6y

Answer

2x - 6y

Answer

4x + 6y

Answer

x + 6y

Question 28

Which of the following is an algebraic expression that represents the area of a rectangle with length l and width w?

Accepted Answer

lw

Answer

l + w

Answer

l / w

Answer

2(l + w)

Question 29

Factor the expression: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)^2

Answer

(x - 2)^2

Answer

x(x - 4)

Question 30

Solve the equation: 2x + 1 = 7

Accepted Answer

x = 3

Answer

x = 6

Answer

x = 4

Answer

x = 5

Question 31

What is the correct order of operations for evaluating algebraic expressions?

Accepted Answer

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (PEMDAS)

Answer

Exponents, Parentheses, Multiplication and Division, Addition and Subtraction

Answer

Parentheses, Multiplication and Division, Addition and Subtraction, Exponents

Answer

Addition and Subtraction, Multiplication and Division, Parentheses, Exponents

Question 32

Identify the constant term in the algebraic expression: 4x^2 - 3xy + 7

Accepted Answer

7

Answer

4

Answer

x

Question 33

Simplify the algebraic expression: (x - 3)^2 - (x + 2)^2

Accepted Answer

-11x

Answer

x

Answer

11x

Answer

-x

Question 34

Find the degree of the algebraic expression: 5x^4 - 2x^2 + 3x - 1

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 35

Which of the following is an algebraic expression?

Accepted Answer

5x + 7

Answer

The result of subtracting 7 from 12

Answer

The difference of two numbers

Answer

x is greater than 3

Question 36

Simplify the expression: 4(2a + 3b) - 2a

Accepted Answer

6a + 12b

Answer

6a + 3b

Answer

8a + 10b

Answer

10ab

Question 37

Which expression represents "twice the sum of a number and 5"?

Accepted Answer

2(x + 5)

Answer

x + 2(5)

Answer

2(x - 5)

Answer

2x + 5

Question 38

Which expression represents the area of a triangle with base b and height h?

Accepted Answer

(1/2)bh

Answer

2bh

Answer

b + h

Answer

bh

Question 39

Identify the factors of the expression x² + 5x + 6.

Accepted Answer

(x + 2)(x + 3)

Answer

(x + 1)(x + 6)

Answer

(x - 2)(x - 3)

Answer

(x - 1)(x - 6)

Question 40

Simplify the expression (3x - 2y) - (x + 4y).

Accepted Answer

2x - 6y

Answer

4x - 2y

Answer

x - 6y

Answer

2x - 2y

Question 41

Solve for x in the equation 2x - 5 = 11.

Accepted Answer

8

Answer

6

Answer

10

Answer

12

Question 42

Which statement best describes the graph of the expression y = -2x + 3?

Accepted Answer

A line with a slope of -2 and a y-intercept of 3

Answer

A hyperbola with an asymptote at y = 3

Answer

A circle with a radius of 3

Answer

A parabola with a vertex at (0, 3)

Question 43

Simplify the algebraic expression: 3x + 5y - 2x + 7y

Accepted Answer

x + 12y

Answer

5x - 12y

Answer

x - 2y

Answer

5x + 2y

Question 44

Evaluate the expression 2a + 3b - c  when a = 2, b = -1, and c = 4.

Accepted Answer

0

Answer

6

Answer

10

Answer

-2

Question 45

Which of the following is an algebraic expression?

Accepted Answer

3x² - 2x + 1

Answer

2x + 3 = 7

Answer

x = 5

Answer

x > 4

Question 46

What is the coefficient of the term -5x² in the expression 7x³ - 5x² + 2x - 1?

Accepted Answer

-5

Answer

5

Answer

1

Answer

2

Question 47

Simplify the expression: 4(2x - 3) + 5x

Accepted Answer

13x - 12

Answer

9x - 12

Answer

8x - 12 + 5x

Answer

8x - 3 + 5x

Question 48

Which of the following is NOT a term in the expression 2a³ - 4ab + 5b²?

Accepted Answer

-4a

Answer

5b²

Answer

2a³

Answer

-4ab

Question 49

Simplify the expression: (x² + 3x - 2) - (2x² - x + 5)

Accepted Answer

-x² + 4x - 7

Answer

3x² + 2x - 3

Answer

-x² + 2x - 7

Answer

-x² + 4x + 3

Question 50

Write an algebraic expression for the phrase 'five times the sum of a number and three'.

Accepted Answer

5(x + 3)

Answer

5 + x + 3

Answer

5x + 3

Answer

5x + 15

Question 51

What is the degree of the algebraic expression 4x³y² - 2xy + 5?

Accepted Answer

5

Answer

3

Answer

2

Answer

1

Question 52

Which expression is equivalent to 3(2x - 1) + 2(x + 4)?

Accepted Answer

8x + 5

Answer

5x + 11

Answer

6x + 5

Answer

6x - 3 + 2x + 4