Polynomials Mid-Unit Review

Simplify & Classify

100

Simplify the polynomial:

6x + 24 + 11x + 2

17x + 26

200

Simplify the polynomial: 

-9p² - 8 + 5p + p²

-8p² + 5p - 8 

300

Classify the polynomial based on the number of terms and degree: 

7w² + 8w - 6

Quadratic (2nd degree) 

Trinomial

400

Simplify the polynomial. Then classify it based on the number of terms and degree: 

7x - 13 + x - 9x³ + 13

-9x³ + 8x 

Cubic (3rd degree) 

Binomia

500

Simplify the polynomial and classify based on the number of terms and degree: 

-x² - 8 - 4x + 6x + 8 + x²

Linear (1st degree) 

Monomial

Adding/Subtracting Polynomials

100

(5x + 3) + (2x + 5)

7x + 8

200

(-2k + 6) - (3k - 14)

-5k + 20

300

(x² - 14) -3(12x -9)

x² - 36x +13

400

(4a² - 5a + 3) -(-a² - 3a + 12)

5a² -2a - 9

500

-12 - 19y² - (y² + 18y -5)

-20y² - 18y - 7

Multiplying/Dividing Polynomials

100

-5t =45

t = -9

200

5(x - 2) - 3 = 42

11

300

[(3x + 5)/4] + 1 = 12

14

400

6(x - 2) + 4(x - 3) + 3(x - 4) = 120

12

500

6/x = 4/x + 3/2

4/3

Random Polynomials

100

Expand:

(-3x)(-6x²)

18x³

200

Expand and simplify: 

2m[m-3(m+2)]

-4m² - 12m

300

Greg is 42. He is 3 years older than Sue. How old is Sue?

Sue is 39 years old

400

Find the root for the equation: 

2(d + 6) = 9(d - 1)

d = 3

500

The total of three sisters' ages is 39. Dina is half as old as Michelle and 3 years younger than Juliette. How old are each sister?

Dina: 9 years old

Michelle: 18 years old

Juliette: 12 years old

Word Problems and Challenging Polynomials

100

Write an equation for the phrase below: 

"The sum of double a number and 6 is 16"

2x + 6 = 16

200

Jerry earns $150 more per week than her roommate Kramer and $100 less than his other roommate George. Together the three friends earn $2050 per week. How much does each person earn per week?

Kramer: $550 per week

Jerry: $700 per week

George: $800 per week

300

(12a³b²c - 30a²bc - 36a²c²)/6a²c

2ab² - 5b - 6c

400

A square and rectangle have the same perimeter. The side length of the square is 2x – 2. The length of the rectangle is x+3 and its width is x – 1. 

Find the lengths of each side. 

Square length = 4 

Rectangle length = 6        Rectangle width = 2

500

The sum of three consecutive integers is 90. Find the integers. 

29, 30, 31