Polynomials

Vocabulary

100

An expression with three terms is called a __________

Trinomial

200

Terms in which the variables or sets of variables are identical even though the coefficients may be different are called ________________

Like terms

300

Greatest common factor is synonymous with _______________ ________________

Monomial extraction

400

The highest exponent of a polynomials monomial term is called its ____________

Degree

500

A polynomial is in __________ _____ when its terms are in order from the greatest power of its variables to its least power

Standard Form

Adding/Subtracting

100

(5x + 6y) + (2x + 8y)

7x + 14y

200

(5c + d) + (3c - 2d)

Classify simplified expression by degree and number of terms

8c - d

1st degree binomial

300

(x² - 5x +4 ) - (3x² + 2x - 5)

Classify simplified expression by degree and number of terms

-2x² - 7x + 9 

Second degree trinomial

400

(3x⁴ - 3xy + 6y²) + (y² - 2x⁴)

Classify simplified expression by degree and number of terms

x⁴ - 7y² - 3xy

4th degree trinomial

500

(25x³y²z + 3x² - 14y⁴) - (20x³y²z - x² + 7y⁴)

Classify the expression by degree and number of terms

5x³y²z - 21y⁴ + 4x²

6th degree trinomial

Multiplying

100

(c+2)(c+8)

c² + 10c + 16 

200

(3d)(4d²f)

12d³f

300

(-8a³b²)²

64a⁶b⁴

400

-5ab[a - (a²b - 3b)]

5a³b² - 5a²b - 15ab²

500

(2-8x)(4 + 7x - 14y²)

112xy² - 56x² - 28y² - 18x + 8

Factoring

100

d² + 16d + 64

(d + 8)(d + 8)

200

25y² - 49z⁴

(5y - 7z²)(5y + 7z²)

300

9a³b + 18a²b² - 6a²b³

3a²b(3a + 6b - 2b²)

400

5rt + 20ru + 2st + 8su

(t + 4u)(5r + 2s)

500

15x² - 13x + 2

(3x - 2)(5x - 1)

Word Problems

100

The cost of the materials for the inner packaging for of a new product is determined by the expression 10x² + 8xy + y². The cost of the outer packaging materials is 4x² - 3xy + 2. Find the total cost of the packaging. 

14x² + 5xy + y² + 2

200

Last week, Pedro worked 17 hours at the pharmacy, where he earns p dollars an hour, and 12 hours in the supermarket, where he earns s dollars an hour. This week, he worked 8 hours at the pharmacy and 20 hours in the supermarket. What were his earnings during the two weeks, in terms of p and s. 

25p + 32s

300

Write and simplify an expression for the area of each rectangle with a length of 2x and a width of 2x + y + z

4x² + 2xy + 2xz

400

A rectangle has an area of 9v²w and a width of 3v. What is its length?

3vw

500

The width of a box is 9in. more than its length. The height of the box is 1 in. less than its length. Write an expression for the volume of the box.

x³ + 8x² - 9x