Expressions

Combining Like terms

100

Define a like term

 either the same variable, two numbers, or variables raised to the same exponent 

200

Are the following like terms 

3x, 4x and 4x²

 No 

300

Why are the following not like terms 

4xy, 3x, and 3x²

Even though they all have x, x is not raised to the same power in all of them. In addition, one has y in its term. 

400

4x+3x+7x-2y-4y

14x-6y

500

-4xy+2x-3xy+4x²-3x+5-2xy+17

4x²-x-7xy+22

Distributive Property

100

Does the following expression require the Distributive  Property? 

4x+7

No 

200

Does the following expression require the distributive Property? Why or Why not? 

6(x-7)

 Yes because there is a number outside of parenthesis which typically indicates we need to distribute. In addition I can not combine anything within my parenthesis 

300

Use the distributive property for the following expression

-4(x-2)

-4x+8

400

Simplify the following expression

-3(x-3x+4)

6x-12

500

Simplify the following expression

-5(x+3) + 2(3x-10) -4(5-x) 

5x-55

Equivalent Expressions

100

Define equivalent expressions

two expressions that are the same or when simplified are the same 

200

are the following expressions equivalent 

3x and x+2x-3x+4x

No

300

Give an expression equivalent to the following 

5x-2x+7 

Answers will vary 

400

create an expression that involves distribution that is equivalent to the following expression 

30x-45

5(6x-9) 

but answers may vary 

500

Create an expression that involves factoring and is equivalent to the following expression 

4x+16x²-8x³

4x(1+4x-2x²)

But answers may vary 

Factoring

100

Define GCF

The largest number that can go into to or more terms 

200

find the GCF Between the following terms 

72 and 36

12

300

Find the GCF for the following terms 

4x⁵ and 16x⁸

4x⁵

400

Factor the following expression 

3x+6x⁴+9

3(x+2x+3) 

500

Factor the following expression 

-15x-5x³+10x⁵

-5x(3+x²-2x⁴)

Structure of a Polynomial

100

Define a polynomial

A term or collection of terms 

200

what are the four  possible components to a polynomial 

Exponents, variables, coefficients, and constants 

300

What are the three common types of polynomials 

 Monomial, Binomial, and trinomial 

400

classify the following polynomials 

3x                   3z-2s

4                     9x+3z-12

45-2x              2x-4x+56

Monomial: 4, 3x 

Binomial: 3z-2s, 45-2x 

Trinomial: 2x-4x+56, 9x+3z-12

500

labe the four components of a polynomial for the following expression 

-6x⁴-3+2xy²+4z-6+w³

Exponents: 4,3,2 

Coefficients: -6, 4, 2 

Constants: -3, -6 

Variables: w, x, y, z