09MATC Manipulating Algebraic Expressions

Question 1

What is an algebraic expression?

Answer 1

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols.

Question 2

True or False: An algebraic expression can contain an equal sign.

Answer 2

False

Question 3

Simplify the expression: 2x + 3x.

Answer 3

5x

Question 4

What is the coefficient in the term 7y?

Answer 4

7

Question 5

Combine like terms: 4a + 5b - 2a + 3b.

Answer 5

2a + 8b

Question 6

Fill in the blank: The expression 5x - 2 is a _____ expression.

Answer 6

linear

Question 7

What is the degree of the polynomial 3x^4 + 2x^2 - x + 7?

Answer 7

4

Question 8

True or False: The expression 2x^2 + 3xy - y^2 is a quadratic expression.

Answer 8

True

Question 9

What do you call numbers in front of variables in an algebraic expression?

Answer 9

Coefficients

Question 10

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

Answer 10

3x + 10

Question 11

What is the result of expanding the expression (x + 2)(x + 3)?

Answer 11

x^2 + 5x + 6

Question 12

Fill in the blank: To factor the expression x^2 - 9, we can write it as _____ and _____ .

Answer 12

(x - 3)(x + 3)

Question 13

What is the first step in simplifying the expression 4(x + 3) - 2(x - 1)?

Answer 13

Distribute the coefficients

Question 14

Combine like terms: 6x^2 + 4x - 3x^2 + 2.

Answer 14

3x^2 + 4x + 2

Question 15

True or False: The expression 5xy + 3x + 2y is a monomial.

Answer 15

False

Question 16

What is the process of rewriting an expression in a simpler form called?

Answer 16

Simplification

Question 17

Expand the expression: 2(x + 5).

Answer 17

2x + 10

Question 18

What is the factored form of 6x^2 - 12x?

Answer 18

6x(x - 2)

Question 19

Fill in the blank: The expression 2x^2 + 4x can be factored to _____ .

Answer 19

2x(x + 2)

Question 20

True or False: The expression 8 - 4x is a polynomial.

Answer 20

True

Question 21

What is the term for the highest power of a variable in a polynomial?

Answer 21

Degree

Question 22

Combine like terms: 7y - 3y + 2y.

Answer 22

6y

Question 23

What is the result of simplifying the expression 5(x - 2) + 3?

Answer 23

5x - 7

Question 24

Fill in the blank: The expression 4x - 4 is a _____ expression.

Answer 24

linear

Question 25

Expand the expression: (x + 1)(x - 1).

Answer 25

x^2 - 1

Question 26

What do you call the result of multiplying a number by itself?

Answer 26

Square

Question 27

True or False: 2x^3 + 3x^2 - x is a cubic polynomial.

Answer 27

True

Question 28

What is the difference between a monomial and a polynomial?

Answer 28

A monomial has one term, while a polynomial has two or more terms.

Question 29

Combine like terms: 10a + 4b - 3a + 2b.

Answer 29

7a + 6b

Question 30

True or False: The expression 9x^2 - 25 can be factored as (3x - 5)(3x + 5).

Answer 30

True

Question 31

What is the result of simplifying the expression 2x + 3x - 5?

Answer 31

5x - 5

Question 32

Fill in the blank: The expression 3x + 5y - 2y can be simplified to _____ .

Answer 32

3x + 3y

Question 33

What is the factored form of the expression x^2 + 5x + 6?

Answer 33

(x + 2)(x + 3)

Question 34

Expand the expression: 4(x - 1) + 2(x + 3).

Answer 34

6x + 10

Question 35

True or False: The expression 7x^2 + 3 is a binomial.

Answer 35

False

Question 36

What is the result of combining the terms 5x^2 - 2x^2 + x?

Answer 36

3x^2 + x

Question 37

Fill in the blank: The expression 12x^2 - 8 can be factored to _____ .

Answer 37

4(3x^2 - 2)

Question 38

What is the degree of the polynomial -2x^3 + 4x^2 - x + 1?

Answer 38

3

Question 39

Combine like terms: 2m + 3n - m + 4n.

Answer 39

m + 7n